#### Chapters

## Chapter 6: Circle

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

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

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

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

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

Find the centre and radius of the circle:

x^{2} + y^{2} = 25

Find the centre and radius of the circle:

(x − 5)^{2} + (y − 3)^{2} = 20

Find the centre and radius of the circle:

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

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

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

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

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

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

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

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

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

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

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

**Find the centre and radius of the following:**

x^{2} + y^{2} − 2x + 4y − 4 = 0

**Find the centre and radius of the following:**

x^{2} + y^{2} − 6x − 8y − 24 = 0

**Find the centre and radius of the following:**

4x^{2} + 4y^{2} − 24x − 8y − 24 = 0

Show that the equation 3x^{2} + 3y^{2} + 12x + 18y − 11 = 0 represents a circle

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

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

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

**Write the parametric equations of the circle:**

x^{2} + y^{2} = 9

**Write the parametric equations of the circle: **

x^{2} + y^{2} + 2x − 4y − 4 = 0

**Write the parametric equations of the circle:**

(x − 3)^{2} + (y + 4)^{2} = 25

**Find the parametric representation of the circle:**

3x^{2} + 3y^{2} − 4x + 6y − 4 = 0

Find the equation of a tangent to the circle x^{2} + y^{2} − 3x + 2y = 0 at the origin

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

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

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

**Choose the correct alternative:**

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

x

^{2}+ y^{2}+ 6x + 6y + 3 = 0x

^{2}+ y^{2}− 6x − 6y − 9 = 0x

^{2}+ y^{2}− 6x − 6y + 9 = 0x

^{2}+ y^{2}− 6x + 6y − 3 = 0

**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

x

^{2}+ y^{2}− 2x + 2y = 40x

^{2}+ y^{2}− 2x + 2y = 40x

^{2}+ y^{2}− 2x + 2y = 47x

^{2}+ y^{2}− 2x − 2y = 40

**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

x

^{2}+ y^{2}− 4x − 10y + 25 = 0x

^{2}+ y^{2}− 4x − 10y − 25 = 0x

^{2}+ y^{2}− 4x + 10y − 25 = 0x

^{2}+ y^{2}+ 4x − 10y + 25 = 0

**Choose the correct alternative:**

The equation of the tangent to the circle x^{2} + y^{2} = 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)`

**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`

**Choose the correct alternative:**

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

5π

10π

25π

100π

**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)`

**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

x

^{2}+ y^{2}= 9a^{2}x

^{2}+ y^{2}= 16a^{2}x

^{2}+ y^{2}= 4a^{2}x

^{2}+ y^{2}= a^{2}

**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)`

**Choose the correct alternative:**

The parametric equations of the circle x^{2} + y^{2} + 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

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

Answer the following :

Find the centre and radius of the circle x^{2} + y^{2} − x +2y − 3 = 0

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

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

Answer the following :

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

Answer the following :

Find the equation of tangent to the circle x^{2} + y^{2} = 64 at the point `"P"((2pi)/3)`

Answer the following :

Find the equation of locus of the point of intersection of perpendicular tangents drawn to the circle x = 5coθ and y = 5sinθ

Answer the following :

Find the equation of the circle concentric with x^{2} + y^{2} – 4x + 6y = 1 and having radius 4 units

Answer the following :

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

x^{2} + y^{2} – 8x + y – 20 = 0

Answer the following :

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

x^{2} + y^{2} – 5x + 13y – 14 = 0

Answer the following :

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

x^{2} + y^{2} – 4x + 10y +20 = 0,

x^{2} + y^{2} + 8x – 6y – 24 = 0.

Answer the following :

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

x^{2} + y^{2} – 4x – 10y + 19 = 0,

x^{2} + y^{2} + 2x + 8y – 23 = 0.

Answer the following :

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

x^{2} + y^{2} – 4x – 4y – 28 = 0,

x^{2} + y^{2} – 4x – 12 = 0

Answer the following :

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

x^{2} + y^{2} + 4x – 12y + 4 = 0,

x^{2} + y^{2} – 2x – 4y + 4 = 0

Answer the following :

Find the length of the tangent segment drawn from the point (5, 3) to the circle x^{2} + y^{2} + 10x – 6y – 17 = 0

Answer the following :

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

x^{2} + y^{2} – 2x + ky – 23 = 0 is `sqrt(10)`

Answer the following :

Find the equation of tangent to Circle x^{2} + y^{2} – 6x – 4y = 0, at the point (6, 4) on it

Answer the following :

Find the equation of tangent to Circle x^{2} + y^{2} = 5, at the point (1, –2) on it

Answer the following :

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

Answer the following :

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

Answer the following :

If the tangent at (3, –4) to the circle x^{2} + y^{2} = 25 touches the circle x^{2} + y^{2} + 8x – 4y + c = 0, find c

Answer the following :

Find the equations of the tangents to the circle x^{2} + y^{2} = 16 with slope –2

Answer the following :

Find the equations of the tangents to the circle x^{2} + y^{2} = 4 which are parallel to 3x + 2y + 1 = 0

Answer the following :

Find the equations of the tangents to the circle x^{2} + y^{2} = 36 which are perpendicular to the line 5x + y = 2

Answer the following :

Find the equations of the tangents to the circle x^{2} + y^{2} – 2x + 8y – 23 = 0 having slope 3

Answer the following :

Find the equation of the locus of a point, the tangents from which to the circle x^{2} + y^{2} = 9 are at right angles.

Answer the following :

Tangents to the circle x^{2} + y^{2} = a^{2} with inclinations, θ_{1} and θ_{2} intersect in P. Find the locus of such that tan θ_{1} + tan θ_{2} = 0

Answer the following :

Tangents to the circle x^{2} + y^{2} = a^{2} with inclinations, θ_{1} and θ_{2} intersect in P. Find the locus of such that cot θ_{1} + cot θ_{2} = 5

Answer the following :

Tangents to the circle x^{2} + y^{2} = a^{2} with inclinations, θ_{1} and θ_{2} intersect in P. Find the locus of such that cot θ_{1} . cot θ_{2} = c

## Chapter 6: Circle

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

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 (Circle) 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 6 Circle are Different Forms of Equation of a Circle, 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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