Maharashtra State BoardHSC Science (General) 11th
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Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 7 - Conic Sections [Latest edition]

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Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com

Chapter 7: Conic Sections

Exercise 7.1Exercise 7.2Exercise 7.3Miscellaneous Exercise 7
Exercise 7.1 [Page 149]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Exercise 7.1 [Page 149]

Exercise 7.1 | Q 1. (i) | Page 149

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co ordinate of end points of latus rectum of the parabola:

5y2 = 24x 

Exercise 7.1 | Q 1. (ii) | Page 149

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co ordinate of end points of latus rectum of the parabola:

y2 = –20x

Exercise 7.1 | Q 1. (iii) | Page 149

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co ordinate of end points of latus rectum of the parabola:

3x2 = 8y

Exercise 7.1 | Q 1. (iv) | Page 149

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co ordinate of end points of latus rectum of the parabola:

x2 = –8y

Exercise 7.1 | Q 1. (v) | Page 149

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co ordinate of end points of latus rectum of the parabola:

3y2 = –16x

Exercise 7.1 | Q 2 | Page 149

Find the equation of the parabola with vertex at the origin, axis along Y-axis and passing through the point (–10,–5)

Exercise 7.1 | Q 3 | Page 149

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (3, 4)

Exercise 7.1 | Q 4 | Page 149

Find the equation of the parabola whose vertex is O(0,0) and focus at (–7,0)

Exercise 7.1 | Q 5. (i) | Page 149

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (1, –6)

Exercise 7.1 | Q 5. (ii) | Page 149

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (2, 3)

Exercise 7.1 | Q 6 (a) | Page 149

For the parabola 3y2 =16x, find the parameter of the point (3, – 4)

Exercise 7.1 | Q 6. (b) | Page 149

For the parabola 3y2 =16x, find the parameter of the point (27, –12)

Exercise 7.1 | Q 7 | Page 149

Find the focal distance of a point on the parabola y2 = 16x whose ordinate is 2 times the abscissa

Exercise 7.1 | Q 8. (i) | Page 149

Find coordinates of the point on the parabola. Also, find focal distance.

y2 = 12x whose parameter is `1/3`

Exercise 7.1 | Q 8. (ii) | Page 149

Find coordinates of the point on the parabola. Also, find focal distance.

2y2 = 7x whose parameter is –2

Exercise 7.1 | Q 9 | Page 149

For the parabola y2 = 4x, find the coordinate of the point whose focal distance is 17

Exercise 7.1 | Q 10 | Page 149

Find length of latus rectum of the parabola y2 = 4ax passing through the point (2, –6)

Exercise 7.1 | Q 11 | Page 149

Find the area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the end points of latus rectum

Exercise 7.1 | Q 12 | Page 149

If a parabolic reflector is 20cm in diameter and 5 cm deep, find its focus

Exercise 7.1 | Q 13 | Page 149

Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x2 – 2x + 3

Exercise 7.1 | Q 14. (i) | Page 149

Find the equation of tangent to the parabola y2 = 12x from the point (2, 5)

Exercise 7.1 | Q 14. (ii) | Page 149

Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)

Exercise 7.1 | Q 15 | Page 149

If the tangent drawn from the point (–6, 9) to the parabola y2 = kx are perpendicular to each other, find k

Exercise 7.1 | Q 16 | Page 149

Two tangents to the parabola y2 = 8x meet the tangents at the vertex in the point P and Q. If PQ = 4, prove that the equation of the locus of the point of intersection of two tangent is y2 = 8(x + 2)

Exercise 7.1 | Q 17 | Page 149

Find the equation of common tangent to the parabola y2 = 4x and x2 = 32y

Exercise 7.1 | Q 18 | Page 149

Find the equation of the locus of a point, the tangents from which to the parabola y2 = 18x are such that some of their slopes is –3

Exercise 7.1 | Q 19 | Page 149

The tower of a bridge, hung in the form of a parabola have their tops 30 meters above the road way and are 200 meters apart. If the cable is 5 meters above the road way at the centre of the bridge, find the length of the vertical supporting cable from the centre

Exercise 7.1 | Q 20 | Page 149

A circle whose centre is (4, –1) passes through the focus of the parabola x2 + 16y = 0.

Show that the circle touches the diretrixs of the parabola

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Exercise 7.2 [Pages 163 - 164]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Exercise 7.2 [Pages 163 - 164]

Exercise 7.2 | Q 1. (a) | Page 163

Answer the following:

Find the

  1. lengths of the principal axes.
  2. co-ordinates of the focii
  3. equations of directrics
  4. length of the latus rectum
  5. distance between focii
  6. distance between directrices of the ellipse:

`x^2/25 + y^2/9` = 1

Exercise 7.2 | Q 1. (b) | Page 163

Find the

  1. lengths of the principal axes.
  2. co-ordinates of the focii
  3. equations of directrics
  4. length of the latus rectum
  5. distance between focii
  6. distance between directrices of the ellipse:

3x2 + 4y2 = 12

Exercise 7.2 | Q 1. (c) | Page 163

Find the

  1. lengths of the principal axes.
  2. co-ordinates of the focii 
  3. equations of directrics 
  4. length of the latus rectum
  5. distance between focii 
  6. distance between directrices of the ellipse:

2x2 + 6y2 = 6

Exercise 7.2 | Q 1. (d) | Page 163

Find the 

  1. lengths of the principal axes. 
  2. co-ordinates of the focii 
  3. equations of directrices 
  4. length of the latus rectum
  5. distance between focii 
  6. distance between directrices of the ellipse:

3x2 + 4y2 = 1

Exercise 7.2 | Q 2. (i) | Page 163

Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6

Exercise 7.2 | Q 2. (ii) | Page 163

Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8

Exercise 7.2 | Q 2. (iii) | Page 163

Find the equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.

Exercise 7.2 | Q 2. (iv) | Page 163

Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.

Exercise 7.2 | Q 2. (v) | Page 163

Find the equation of the ellipse in standard form if the distance between foci is 6 and the distance between directrix is `50/3`.

Exercise 7.2 | Q 2. (vi) | Page 163

Find the equation of the ellipse in standard form if the latus rectum has length 6 and foci are (+2, 0).

Exercise 7.2 | Q 2. (vii) | Page 163

Find the equation of the ellipse in standard form if passing through the points (−3, 1) and (2, −2)

Exercise 7.2 | Q 2. (viii) | Page 163

Find the equation of the ellipse in standard form if the dist. between its directrix is 10 and which passes through `(-sqrt(5), 2)`.

Exercise 7.2 | Q 2. (ix) | Page 163

Find the equation of the ellipse in standard form if eccentricity is `2/3` and passes through `(2, −5/3)`.

Exercise 7.2 | Q 3 | Page 163

Find the eccentricity of an ellipse, if the length of its latus rectum is one third of its minor axis

Exercise 7.2 | Q 4 | Page 163

Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci

Exercise 7.2 | Q 5 | Page 163

Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16

Exercise 7.2 | Q 6 | Page 163

A tangent having slope `–1/2` to the ellipse 3x2 + 4y2 = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle

Exercise 7.2 | Q 7 | Page 163

Show that the line x – y = 5 is a tangent to the ellipse 9x2 + 16y2 = 144. Find the point of contact

Exercise 7.2 | Q 8 | Page 163

Show that the line 8y + x = 17 touches the ellipse x2 + 4y2 = 17. Find the point of contact

Exercise 7.2 | Q 9 | Page 163

Determine whether the line `x + 3ysqrt(2)` = 9 is a tangent to the ellipse `x^2/9 + y^2/4` = 1. If so, find the co-ordinates of the pt of contact

Exercise 7.2 | Q 10 | Page 163

Find k, if the line 3x + 4y + k = 0 touches 9x2 + 16y2 = 144

Exercise 7.2 | Q 11. (i) | Page 163

Find the equation of the tangent to the ellipse `x^2/5 + y^2/4` = 1 passing through the point (2, –2)

Exercise 7.2 | Q 11. (ii) | Page 163

Find the equation of the tangent to the ellipse 4x2 + 7y2 = 28 from the point (3, –2).

Exercise 7.2 | Q 11. (iii) | Page 163

Find the equation of the tangent to the ellipse 2x2 + y2 = 6 from the point (2, 1).

Exercise 7.2 | Q 11. (iv) | Page 163

Find the equation of the tangent to the ellipse x2 + 4y2 = 9 which are parallel to the line 2x + 3y – 5 = 0.

Exercise 7.2 | Q 11. (v) | Page 163

Find the equation of the tangent to the ellipse `x^2/25 + y^2/4` = 1 which are parallel to the line x + y + 1 = 0.

Exercise 7.2 | Q 11. (vi) | Page 163

Find the equation of the tangent to the ellipse 5x2 + 9y2 = 45 which are ⊥ to the line 3x + 2y + y = 0.

Exercise 7.2 | Q 11. (vii) | Page 163

Find the equation of the tangent to the ellipse x2 + 4y2 = 20, ⊥ to the line 4x + 3y = 7.

Exercise 7.2 | Q 12 | Page 163

Find the equation of the locus of a point the tangents form which to the ellipse 3x2 + 5y2 = 15 are at right angles

Exercise 7.2 | Q 13 | Page 164

Tangents are drawn through a point P to the ellipse 4x2 + 5y2 = 20 having inclinations θ1 and θ2 such that tan θ1 + tan θ2 = 2. Find the equation of the locus of P

Exercise 7.2 | Q 14 | Page 164

Show that the locus of the point of intersection of tangents at two points on an ellipse, whose eccentric angles differ by a constant, is an ellipse

Exercise 7.2 | Q 15 | Page 164

P and Q are two points on the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 with eccentric angles θ1 and θ2. Find the equation of the locus of the point of intersection of the tangents at P and Q if θ1 + θ2 = `π/2`

Exercise 7.2 | Q 16 | Page 164

The eccentric angles of two points P and Q the ellipse 4x2 + y2 = 4 differ by `(2pi)/3`. Show that the locus of the point of intersection of the tangents at P and Q is the ellipse 4x2 + y2 = 16

Exercise 7.2 | Q 17 | Page 164

Find the equations of the tangents to the ellipse `x^2/16 + y^2/9` = 1, making equal intercepts on co-ordinate axes

Exercise 7.2 | Q 18 | Page 164

A tangent having slope `–1/2` to the ellipse 3x2 + 4y2 = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle

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Exercise 7.3 [Pages 174 - 175]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Exercise 7.3 [Pages 174 - 175]

Exercise 7.3 | Q 1. (i) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = 1

Exercise 7.3 | Q 1. (ii) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = – 1

Exercise 7.3 | Q 1. (iii) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

16x2 – 9y2 = 144

Exercise 7.3 | Q 1. (iv) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

21x2 – 4y2 = 84

Exercise 7.3 | Q 1. (v) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

3x2 – y2 = 4

Exercise 7.3 | Q 1. (vi) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

x2 – y2 = 16

Exercise 7.3 | Q 1. (vii) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`y^2/25 - x^2/9` = 1

Exercise 7.3 | Q 1. (viii) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`y^2/25 - x^2/144` = 1

Exercise 7.3 | Q 1. (ix) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/100 - y^2/25` = + 1

Exercise 7.3 | Q 1. (x) | Page 174

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

x = 2 sec θ, y = `2sqrt(3) tan theta`

Exercise 7.3 | Q 2 | Page 174

Find the equation of the hyperbola with centre at the origin, length of conjugate axis 10 and one of the foci (–7, 0)

Exercise 7.3 | Q 3 | Page 174

Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x2 – 3y2 = 3

Exercise 7.3 | Q 4 | Page 174

If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively, prove that `1/"e"^2 + 1/("e"^"'")^2` = 1

Exercise 7.3 | Q 5. (i) | Page 174

Find the equation of the hyperbola referred to its principal axes:

whose distance between foci is 10 and eccentricity `5/2`

Exercise 7.3 | Q 5. (ii) | Page 174

Find the equation of the hyperbola referred to its principal axes:

whose distance between foci is 10 and length of conjugate axis 6

Exercise 7.3 | Q 5. (iii) | Page 174

Find the equation of the hyperbola referred to its principal axes:

whose distance between directrices is `8/3` and eccentricity is `3/2`

Exercise 7.3 | Q 5. (iv) | Page 175

Find the equation of the hyperbola referred to its principal axes:

whose length of conjugate axis = 12 and passing through (1, – 2)

Exercise 7.3 | Q 5. (v) | Page 175

Find the equation of the hyperbola referred to its principal axes:

which passes through the points (6, 9) and (3, 0)

Exercise 7.3 | Q 5. (vi) | Page 175

Find the equation of the hyperbola referred to its principal axes:

whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)

Exercise 7.3 | Q 5. (vii) | Page 175

Find the equation of the hyperbola referred to its principal axes:

whose foci are at (±2, 0) and eccentricity `3/2`

Exercise 7.3 | Q 5. (viii) | Page 175

Find the equation of the hyperbola referred to its principal axes:

whose length of transverse and conjugate axis are 6 and 9 respectively

Exercise 7.3 | Q 5. (ix) | Page 175

Find the equation of the hyperbola referred to its principal axes:

whose length of transverse axis is 8 and distance between foci is 10

Exercise 7.3 | Q 6. (i) | Page 175

Find the equation of the tangent to the hyperbola:

3x2 – y2 = 4 at the point `(2, 2sqrt(2))`

Exercise 7.3 | Q 6. (ii) | Page 175

Find the equation of the tangent to the hyperbola:

3x2 – y2 = 12 at the point (4, 3)

Exercise 7.3 | Q 6. (iii) | Page 175

Find the equation of the tangent to the hyperbola:

`x^2/144 - y^2/25` = 1 at the point whose eccentric angle is `pi/3`

Exercise 7.3 | Q 6. (iv) | Page 175

Find the equation of the tangent to the hyperbola:

`x^2/16 - y^2/9` = 1 at the point in a first quadratures whose ordinate is 3

Exercise 7.3 | Q 6. (v) | Page 175

Find the equation of the tangent to the hyperbola:

9x2 – 16y2 = 144 at the point L of latus rectum in the first quadrant

Exercise 7.3 | Q 7 | Page 175

Show that the line 3x – 4y + 10 = 0 is tangent till the hyperbola x2 – 4y2 = 20. Also find the point of contact

Exercise 7.3 | Q 8 | Page 175

If the 3x – 4y = k touches the hyperbola `x^2/5 - (4y^2)/5` = 1 then find the value of k

Exercise 7.3 | Q 9 | Page 175

Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes

Exercise 7.3 | Q 10 | Page 175

Find the equations of the tangents to the hyperbola 5x2 – 4y2 = 20 which are parallel to the line 3x + 2y + 12 = 0

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Miscellaneous Exercise 7 [Pages 176 - 177]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Miscellaneous Exercise 7 [Pages 176 - 177]

Miscellaneous Exercise 7 | Q I. (1) | Page 176

Select the correct option from the given alternatives:

The line y = mx + 1 is a tangent to the parabola y2 = 4x, if m is _______

  • 1

  • 2

  • 3

  • 4

Miscellaneous Exercise 7 | Q I. (2) | Page 176

Select the correct option from the given alternatives:

The length of latus rectum of the parabola x2 – 4x – 8y + 12 = 0 is _________

  • 4

  • 6

  • 8

  • 10

Miscellaneous Exercise 7 | Q I. (3) | Page 176

Select the correct option from the given alternatives:

If the focus of the parabola is (0, –3) its directrix is y = 3 then its equation is

  • x2 = – 12y

  • x2 = 12y

  • y2 = 12x

  • y2 = −12x

Miscellaneous Exercise 7 | Q I. (4) | Page 176

Select the correct option from the given alternatives:

The coordinates of a point on the parabola y2 = 8x whose focal distance is 4 are _______

  • `(1/2, ±2)`

  • `(1, ±2sqrt(2))`

  • (2, ± 4)

  • none of these

Miscellaneous Exercise 7 | Q I. (5) | Page 176

Select the correct option from the given alternatives:

The endpoints of latus rectum of the parabola y2 = 24x are _______

  • (6, ±12)

  • (12, ±6)

  • (6, ±6)

  • none of these

Miscellaneous Exercise 7 | Q I. (6) | Page 176

Select the correct option from the given alternatives:

Equation of the parabola with vertex at the origin and directrix x + 8 = 0 is __________

  • y2 = 8x

  • y2 = 32x

  • y2 = 16x

  • x2 = 32y

Miscellaneous Exercise 7 | Q I. (7) | Page 176

Select the correct option from the given alternatives:

The area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the endpoints of its latus rectum is _________

  • 22 sq.units

  • 20 sq.units

  • 18 sq.units

  • 14 sq.units

Miscellaneous Exercise 7 | Q I. (8) | Page 176

Select the correct option from the given alternatives:

If `"P"(pi/4)` is any point on he ellipse 9x2 + 25y2 = 225. S and S1 are its foci then SP.S1P =

  • 13

  • 14

  • 17

  • 19

Miscellaneous Exercise 7 | Q I. (9) | Page 176

Select the correct option from the given alternatives:

The equation of the parabola having (2, 4) and (2, –4) as endpoints of its latus rectum is _________

  • y2 = 4x

  • y2 = 8x

  • y2 = –16x

  • x2 = 8y

Miscellaneous Exercise 7 | Q I. (10) | Page 177

Select the correct option from the given alternatives:

If the parabola y2 = 4ax passes through (3, 2) then the length of its latus rectum is ________

  • `2/3`

  • `4/3`

  • `1/3`

  • 4

Miscellaneous Exercise 7 | Q I. (11) | Page 177

Select the correct option from the given alternatives

The eccentricity of rectangular hyperbola is

  • `1/2`

  • `1/(2 1/2)`

  • `2 1/2`

  • `1/(3 1/2)`

Miscellaneous Exercise 7 | Q I. (12) | Page 177

Select the correct option from the given alternatives:

The equation of the ellipse having foci (+4, 0) and eccentricity `1/3` is

  • 9x2 + 16y2 = 144

  • 144x2 + 9y2 = 1296

  • 128x2 + 144y2 = 18432

  • 144x2 + 128y2 = 18432

Miscellaneous Exercise 7 | Q I. (13) | Page 177

Select the correct option from the given alternatives:

The equation of the ellipse having eccentricity `sqrt(3)/2` and passing through (− 8, 3) is

  • 4x2 + y2 = 4

  • x2 + 4y2 = 100

  • 4x2 + y2 = 100

  • x2 + 4y2 = 4

Miscellaneous Exercise 7 | Q I. (14) | Page 177

Select the correct option from the given alternatives:

If the line 4x − 3y + k = 0 touches the ellipse 5x2 + 9y2 = 45 then the value of k is

  • + 21

  • `± 3sqrt(21)`

  • + 3

  • + 3(21)

Miscellaneous Exercise 7 | Q I. (15) | Page 177

Select the correct option from the given alternatives:

The equation of the ellipse is 16x2 + 25y2 = 400. The equations of the tangents making an angle of 180° with the major axis are

  • x = 4

  • y = ± 4

  • x = – 4

  • x = ± 5

Miscellaneous Exercise 7 | Q I. (16) | Page 177

Select the correct option from the given alternatives:

The equation of the tangent to the ellipse 4x2 + 9y2 = 36 which is perpendicular to the 3x + 4y = 17 is,

  • y = 4x + 6

  • 3y + 4x = 6

  • 3y = `4x + 6sqrt(5)`

  • 3y = x + 25

Miscellaneous Exercise 7 | Q I. (17) | Page 177

Select the correct option from the given alternatives:

Eccentricity of the hyperbola 16x2 − 3y2 − 32x − 12y − 44 = 0 is

  • `sqrt(17/3)`

  • `sqrt(19/3)`

  • `sqrt(19)/3`

  • `sqrt(17)/3`

Miscellaneous Exercise 7 | Q I. (18) | Page 177

Select the correct option from the given alternatives:

Centre of the ellipse 9x2 + 5y2 − 36x − 50y − 164 = 0 is at

  • (2, 5)

  • (1, −2)

  • (−2, 1)

  • (0, 0)

Miscellaneous Exercise 7 | Q I. (19) | Page 177

Select the correct option from the given alternatives:

If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is

  • (1, 2)

  • (2, 3)

  • (3, 2)

  • (−2, −3)

Miscellaneous Exercise 7 | Q I. (20) | Page 177

Select the correct option from the given alternatives:

The foci of hyperbola 4x2 − 9y2 − 36 = 0 are

  • `(± sqrt(13), 0)`

  • `(± sqrt(11), 0)`

  • `(± sqrt(12), 0)`

  • ` (0,± sqrt(12))`

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Miscellaneous Exercise 7 [Pages 177 - 178]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Miscellaneous Exercise 7 [Pages 177 - 178]

Miscellaneous Exercise 7 | Q II. (1) (i) | Page 177

Answer the following:

For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:

2y2 = 17x

Miscellaneous Exercise 7 | Q II. (1) (ii) | Page 177

Answer the following:

For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:

5x2 = 24y

Miscellaneous Exercise 7 | Q II. (2) (i) | Page 177

Answer the following:

Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is 2

Miscellaneous Exercise 7 | Q II. (2) (ii) | Page 177

Answer the following:

Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is −3

Miscellaneous Exercise 7 | Q 2.03 | Page 177

Answer the following:

Find the co-ordinates of a point of the parabola y2 = 8x having focal distance 10

Miscellaneous Exercise 7 | Q 2.04 | Page 177

Answer the following:

Find the equation of the tangent to the parabola y2 = 9x at the point (4, −6) on it

Miscellaneous Exercise 7 | Q 2.05 | Page 177

Answer the following:

Find the equation of the tangent to the parabola y2 = 8x at t = 1 on it

Miscellaneous Exercise 7 | Q 2.06 | Page 177

Answer the following:

Find the equations of the tangents to the parabola y2 = 9x through the point (4,10)

Miscellaneous Exercise 7 | Q 2.07 | Page 177

Answer the following:

Show that the two tangents drawn to the parabola y2 = 24x from the point (−6, 9) are at the right angle

Miscellaneous Exercise 7 | Q 2.08 | Page 177

Answer the following:

Find the equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x + 2y + 5 = 0. Find its point of contact

Miscellaneous Exercise 7 | Q 2.09 | Page 177

Answer the following:

A line touches the circle x2 + y2 = 2 and the parabola y2 = x. Show that its equation is y = ± (x+2)

Miscellaneous Exercise 7 | Q 2.1 | Page 177

Two tangents to the parabola y2 = 8x meet the tangents at the vertex in the point P and Q. If PQ = 4, prove that the equation of the locus of the point of intersection of two tangent is y2 = 8(x + 2)

Miscellaneous Exercise 7 | Q II. (11) (i) | Page 178

Answer the following:

The slopes of the tangents drawn from P to the parabola y2 = 4ax are m1 and m2 , show that  m1 − m2 = k 

Miscellaneous Exercise 7 | Q II. (11) (ii) | Page 178

Answer the following:

The slopes of the tangents drawn from P to the parabola y2 = 4ax are m1 and m2 , show that  `("m"_1 /"m"_2)` = k, where k is a constant.

Miscellaneous Exercise 7 | Q 2.12 | Page 178

Answer the following:

The tangent at point P on the parabola y2 = 4ax meets the y-axis in Q. If S is the focus, show that SP subtends a right angle at Q

Miscellaneous Exercise 7 | Q II. (13) (i) | Page 178

Answer the following:

Find the

  1. lengths of the principal axes.
  2. co-ordinates of the focii
  3. equations of directrics
  4. length of the latus rectum
  5. distance between focii
  6. distance between directrices of the ellipse:

`x^2/25 + y^2/9` = 1

Miscellaneous Exercise 7 | Q II. (13) (ii) | Page 178

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

16x2 + 25y2 = 400

Miscellaneous Exercise 7 | Q II. (13) (iii) | Page 178

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

`x^2/144 - y^2/25` = 1

Miscellaneous Exercise 7 | Q II. (13) (iv) | Page 178

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

x2 − y2 = 16

Miscellaneous Exercise 7 | Q II. (14) (i) | Page 178

Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6

Miscellaneous Exercise 7 | Q II. (14) (iii) | Page 178

Find the equation of the ellipse in standard form if passing through the points (−3, 1) and (2, −2)

Miscellaneous Exercise 7 | Q II. (14) (ii) | Page 178

Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8

Miscellaneous Exercise 7 | Q 2.15 | Page 178

Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci

Miscellaneous Exercise 7 | Q 2.16 | Page 178

Answer the following:

For the hyperbola `x^2/100−y^2/25` = 1, prove that SA. S'A = 25, where S and S' are the foci and A is the vertex

Miscellaneous Exercise 7 | Q 2.17 | Page 178

Find the equation of the tangent to the ellipse `x^2/5 + y^2/4` = 1 passing through the point (2, –2)

Miscellaneous Exercise 7 | Q 2.18 | Page 178

Answer the following:

Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)

Miscellaneous Exercise 7 | Q 2.19 | Page 178

Show that the line 8y + x = 17 touches the ellipse x2 + 4y2 = 17. Find the point of contact

Miscellaneous Exercise 7 | Q 2.2 | Page 178

Tangents are drawn through a point P to the ellipse 4x2 + 5y2 = 20 having inclinations θ1 and θ2 such that tan θ1 + tan θ2 = 2. Find the equation of the locus of P

Miscellaneous Exercise 7 | Q 2.21 | Page 178

Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16

Miscellaneous Exercise 7 | Q II. (22) (i) | Page 178

Answer the following:

Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13

Miscellaneous Exercise 7 | Q II. (22) (ii) | Page 178

Answer the following:

Find the equation of the hyperbola in the standard form if eccentricity is `3/2` and distance between foci is 12

Miscellaneous Exercise 7 | Q II. (22) (iii) | Page 178

Answer the following:

Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5

Miscellaneous Exercise 7 | Q II. (23) (i) | Page 178

Answer the following:

Find the equation of the tangent to the hyperbola 7x2 − 3y2 = 51 at (−3, −2)

Miscellaneous Exercise 7 | Q II. (23) (ii) | Page 178

Answer the following:

Find the equation of the tangent to the hyperbola x = 3 secθ, y = 5 tanθ at θ = `pi/3`

Miscellaneous Exercise 7 | Q II. (23) (iii) | Page 178

Answer the following:

Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)

Miscellaneous Exercise 7 | Q 2.24 | Page 178

Answer the following:

Show that the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24. Find the point of contact

Miscellaneous Exercise 7 | Q 2.25 | Page 178

Answer the following:

Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0

Miscellaneous Exercise 7 | Q 2.26 | Page 178

Answer the following:

Two tangents to the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 make angles θ1, θ2, with the transverse axis. Find the locus of their point of intersection if tanθ1 + tanθ2 = k

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Chapter 7: Conic Sections

Exercise 7.1Exercise 7.2Exercise 7.3Miscellaneous Exercise 7
Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 7 - Conic Sections

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 7 (Conic Sections) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 7 Conic Sections are Double Cone, Conic Sections, Parabola, Ellipse, Hyperbola.

Using Balbharati 11th solutions Conic Sections exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 11th prefer Balbharati Textbook Solutions to score more in exam.

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