# Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 - Circle [Latest edition]

## Chapter 6: Circle

Exercise 6.1Exercise 6.2Exercise 6.3Miscellaneous Exercise 6
Exercise 6.1 [Page 129]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Circle Exercise 6.1 [Page 129]

Exercise 6.1 | Q 1. (i) | Page 129

Find the equation of the circle with centre at origin and radius 4.

Exercise 6.1 | Q 1. (ii) | Page 129

Find the equation of the circle with centre at (−3, −2) and radius 6.

Exercise 6.1 | Q 1. (iii) | Page 129

Find the equation of the circle with centre at (2, −3) and radius 5.

Exercise 6.1 | Q 1. (iv) | Page 129

Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)

Exercise 6.1 | Q 2. (i) | Page 129

Find the centre and radius of the circle:

x2 + y2 = 25

Exercise 6.1 | Q 2. (ii) | Page 129

Find the centre and radius of the circle:

(x − 5)2 + (y − 3)2 = 20

Exercise 6.1 | Q 2. (iii) | Page 129

Find the centre and radius of the circle:

(x - 1/2)^2 + (y + 1/3)^2 = 1/36

Exercise 6.1 | Q 3. (i) | Page 129

Find the equation of the circle with centre at (a, b) touching the Y-axis

Exercise 6.1 | Q 3. (ii) | Page 129

Find the equation of the circle with centre at (–2, 3) touching the X-axis.

Exercise 6.1 | Q 3. (iii) | Page 129

Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.

Exercise 6.1 | Q 3. (iv) | Page 129

Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0

Exercise 6.1 | Q 4 | Page 129

Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9

Exercise 6.1 | Q 5 | Page 129

If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre

Exercise 6.1 | Q 6 | Page 129

Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.

Exercise 6.1 | Q 7 | Page 129

Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes

Exercise 6.1 | Q 8 | Page 129

Find the equation of a circle passing through the points (1,−4), (5,2) and having its centre on the line x − 2y + 9 = 0

Exercise 6.2 [Page 132]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Circle Exercise 6.2 [Page 132]

Exercise 6.2 | Q 1. (i) | Page 132

Find the centre and radius of the following:

x2 + y2 − 2x + 4y − 4 = 0

Exercise 6.2 | Q 1. (ii) | Page 132

Find the centre and radius of the following:

x2 + y2 − 6x − 8y − 24 = 0

Exercise 6.2 | Q 1. (iii) | Page 132

Find the centre and radius of the following:

4x2 + 4y2 − 24x − 8y − 24 = 0

Exercise 6.2 | Q 2 | Page 132

Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle

Exercise 6.2 | Q 3 | Page 132

Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)

Exercise 6.2 | Q 4 | Page 132

Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic

Exercise 6.3 [Page 135]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Circle Exercise 6.3 [Page 135]

Exercise 6.3 | Q 1. (i) | Page 135

Write the parametric equations of the circle:

x2 + y2 = 9

Exercise 6.3 | Q 1. (ii) | Page 135

Write the parametric equations of the circle:

x2 + y2 + 2x − 4y − 4 = 0

Exercise 6.3 | Q 1. (iii) | Page 135

Write the parametric equations of the circle:

(x − 3)2 + (y + 4)2 = 25

Exercise 6.3 | Q 2 | Page 135

Find the parametric representation of the circle:

3x2 + 3y2 − 4x + 6y − 4 = 0

Exercise 6.3 | Q 3 | Page 135

Find the equation of a tangent to the circle x2 + y2 − 3x + 2y = 0 at the origin

Exercise 6.3 | Q 4 | Page 135

Show that the line 7x − 3y − 1 = 0 touches the circle x2 + y2 + 5x − 7y + 4 = 0 at point (1, 2)

Exercise 6.3 | Q 5 | Page 135

Find the equation of tangent to the circle x2 + y2 − 4x + 3y + 2 = 0 at the point (4, −2)

Miscellaneous Exercise 6 [Pages 136 - 137]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Circle Miscellaneous Exercise 6 [Pages 136 - 137]

Miscellaneous Exercise 6 | Q I. (1) | Page 136

Choose the correct alternative:

Equation of a circle which passes through (3, 6) and touches the axes is

• x2 + y2 + 6x + 6y + 3 = 0

• x2 + y2 − 6x − 6y − 9 = 0

• x2 + y2 − 6x − 6y + 9 = 0

• x2 + y2 − 6x + 6y − 3 = 0

Miscellaneous Exercise 6 | Q I. (2) | Page 136

Choose the correct alternative:

If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle

• x2 + y2 − 2x + 2y = 40

• x2 + y2 − 2x + 2y = 40

• x2 + y2 − 2x + 2y = 47

• x2 + y2 − 2x − 2y = 40

Miscellaneous Exercise 6 | Q I. (3) | Page 136

Choose the correct alternative:

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0

• x2 + y2 − 4x − 10y + 25 = 0

• x2 + y2 − 4x − 10y − 25 = 0

• x2 + y2 − 4x + 10y − 25 = 0

• x2 + y2 + 4x − 10y + 25 = 0

Miscellaneous Exercise 6 | Q I. (4) | Page 136

Choose the correct alternative:

The equation of the tangent to the circle x2 + y2 = 4 which are parallel to x + 2y + 3 = 0 are

• x − 2y = 2

• x + 2y = ± 2sqrt(3)

• x + 2y = ± 2sqrt(5)

• x − 2y = ± 2sqrt(5)

Miscellaneous Exercise 6 | Q I. (5) | Page 136

Choose the correct alternative:

If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle

• 3/4

• 4/3

• 1/4

• 7/4

Miscellaneous Exercise 6 | Q I. (6) | Page 137

Choose the correct alternative:

Area of the circle centre at (1, 2) and passing through (4, 6) is

• 10π

• 25π

• 100π

Miscellaneous Exercise 6 | Q I. (7) | Page 137

Choose the correct alternative:

If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre

• ((-"a")/2, (-"b")/2)

• ("a"/2, (-"b")/2)

• ((-"a")/2, "b"/2)

• ("a"/2, "b"/2)

Miscellaneous Exercise 6 | Q I. (8) | Page 137

Choose the correct alternative:

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

• x2 + y2 = 9a2

• x2 + y2 = 16a2

• x2 + y2 = 4a2

• x2 + y2 = a2

Miscellaneous Exercise 6 | Q I. (9) | Page 137

Choose the correct alternative:

A pair of tangents are drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60°. The area enclosed by these tangents and the area of the circle is

• 2/sqrt(3) - pi/6

• sqrt(3) - pi/3

• pi/3 - sqrt(3)/6

• sqrt(3)(1 - pi/6)

Miscellaneous Exercise 6 | Q I. (10) | Page 137

Choose the correct alternative:

The parametric equations of the circle x2 + y2 + mx + my = 0 are

• x = (-"m")/2 + "m"/sqrt(2)costheta, y = (-"m")/2 + "m"/sqrt(2)sintheta

• x = (-"m")/2 + "m"/sqrt(2)costheta, y = (+"m")/2 + "m"/sqrt(2)sintheta

• x = 0 , y = 0

• x = mcosθ ; y = msinθ

Miscellaneous Exercise 6 [Pages 137 - 138]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Circle Miscellaneous Exercise 6 [Pages 137 - 138]

Miscellaneous Exercise 6 | Q II. (1) | Page 137

Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0

Miscellaneous Exercise 6 | Q II. (2) | Page 137

Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ

Miscellaneous Exercise 6 | Q II. (3) | Page 137

Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0

Miscellaneous Exercise 6 | Q II. (4) | Page 137

Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively

Miscellaneous Exercise 6 | Q II. (5) | Page 137

Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic

Miscellaneous Exercise 6 | Q II. (6) | Page 137

The line 2x − y + 6 = 0 meets the circle x2 + y2 + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.

Miscellaneous Exercise 6 | Q II. (7) | Page 137

Show that x = −1 is a tangent to circle x2 + y2 − 2 = 0 at (−1, 1)

Miscellaneous Exercise 6 | Q II. (8) | Page 137

Find the equation of tangent to the circle x2 + y2 = 64 at the point "P"((2pi)/3)

Miscellaneous Exercise 6 | Q II. (9) | Page 137

Find the equation of locus of the point of intersection of perpendicular tangents drawn to the circle x = 5 cos θ and y = 5 sin θ

Miscellaneous Exercise 6 | Q II. (10) | Page 137

Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units

Miscellaneous Exercise 6 | Q II. (11) (i) | Page 137

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x2 + y2 – 8x + y – 20 = 0

Miscellaneous Exercise 6 | Q II. (11) (ii) | Page 137

Find the lengths of the intercepts made on the co-ordinate axes, by the circle:

x2 + y2 – 5x + 13y – 14 = 0

Miscellaneous Exercise 6 | Q II. (12) (i) | Page 138

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x2 + y2 – 4x + 10y +20 = 0,

x2 + y2 + 8x – 6y – 24 = 0.

Miscellaneous Exercise 6 | Q II. (12) (ii) | Page 138

Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:

x2 + y2 – 4x – 10y + 19 = 0,

x2 + y2 + 2x + 8y – 23 = 0.

Miscellaneous Exercise 6 | Q II. (13) (i) | Page 138

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x2 + y2 – 4x – 4y – 28 = 0,

x2 + y2 – 4x – 12 = 0

Miscellaneous Exercise 6 | Q II. (13) (ii) | Page 138

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:

x2 + y2 + 4x – 12y + 4 = 0,

x2 + y2 – 2x – 4y + 4 = 0

Miscellaneous Exercise 6 | Q II. (14) | Page 138

Find the length of the tangent segment drawn from the point (5, 3) to the circle x2 + y2 + 10x – 6y – 17 = 0

Miscellaneous Exercise 6 | Q II. (15) | Page 138

Find the value of k, if the length of the tangent segment from the point (8, –3) to the circle

x2 + y2 – 2x + ky – 23 = 0 is sqrt(10)

Miscellaneous Exercise 6 | Q 2.16 | Page 138

Find the equation of tangent to Circle x2 + y2 – 6x – 4y = 0, at the point (6, 4) on it

Miscellaneous Exercise 6 | Q II. (17) | Page 138

Find the equation of tangent to Circle x2 + y2 = 5, at the point (1, –2) on it

Miscellaneous Exercise 6 | Q II. (18) | Page 138

Find the equation of the tangent to Circle x = 5 cosθ. y = 5 sinθ, at the point θ = pi/3 on it

Miscellaneous Exercise 6 | Q II. (19) | Page 138

Show that 2x + y + 6 = 0 is a tangent to x2 + y2 + 2x – 2y – 3 = 0. Find its point of contact

Miscellaneous Exercise 6 | Q II. (20) | Page 138

If the tangent at (3, –4) to the circle x2 + y2 = 25 touches the circle x2 + y2 + 8x – 4y + c = 0, find c

Miscellaneous Exercise 6 | Q II. (21) | Page 138

Find the equations of the tangents to the circle x2 + y2 = 16 with slope –2

Miscellaneous Exercise 6 | Q II. (22) | Page 138

Find the equations of the tangents to the circle x2 + y2 = 4 which are parallel to 3x + 2y + 1 = 0

Miscellaneous Exercise 6 | Q II. (23) | Page 138

Find the equations of the tangents to the circle x2 + y2 = 36 which are perpendicular to the line 5x + y = 2

Miscellaneous Exercise 6 | Q II. (24) | Page 138

Find the equations of the tangents to the circle x2 + y2 – 2x + 8y – 23 = 0 having slope 3

Miscellaneous Exercise 6 | Q II. (25) | Page 138

Find the equation of the locus of a point, the tangents from which to the circle x2 + y2 = 9 are at right angles.

Miscellaneous Exercise 6 | Q II. (26) (i) | Page 138

Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that tan θ1 + tan θ2 = 0

Miscellaneous Exercise 6 | Q II. (26) (ii) | Page 138

Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 + cot θ2 = 5

Miscellaneous Exercise 6 | Q II. (26) (iii) | Page 138

Tangents to the circle x2 + y2 = a2 with inclinations, θ1 and θ2 intersect in P. Find the locus of such that cot θ1 . cot θ2 = c

## Chapter 6: Circle

Exercise 6.1Exercise 6.2Exercise 6.3Miscellaneous Exercise 6

## Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 - Circle

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Concepts covered in Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 Circle are Different Forms of Equation of a Circle, General Equation of a Circle, Parametric Form of a Circle, Tangent, Condition of tangency, Tangents from a Point to the Circle, Director circle.

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