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

## 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 20 cm 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 roadway and are 200 meters apart. If the cable is 5 meters above the roadway at the centre of the bridge, find the length of the vertical supporting cable 30 meters 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 directrix of the parabola.

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

Find the

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

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 – 4y2 = 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

Miscellaneous Exercise 7 [Pages 176 - 178]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 7 Conic Sections Miscellaneous Exercise 7 [Pages 176 - 178]

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))

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

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

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

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

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

Miscellaneous Exercise 7 | Q 2.03 | Page 177

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

Miscellaneous Exercise 7 | Q 2.04 | Page 177

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

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

Miscellaneous Exercise 7 | Q 2.06 | Page 177

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

Miscellaneous Exercise 7 | Q 2.07 | Page 177

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

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

A line touches the circle x2 + y2 = 2 and the parabola y2 = 8x. 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

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

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

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

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

Find the

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 tan θ1 + tan θ2 = k

## Chapter 7: Conic Sections

Exercise 7.1Exercise 7.2Exercise 7.3Miscellaneous Exercise 7

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

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