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 6 - Circle [Latest edition]

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Chapters

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

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

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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

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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)

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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

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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

Answer the following :

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

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

Answer the following :

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

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

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

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

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

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

Answer the following :

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

Answer the following :

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

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

Answer the following :

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

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

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

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

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

Answer the following :

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

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Chapter 6: Circle

Exercise 6.1Exercise 6.2Exercise 6.3Miscellaneous Exercise 6
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 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.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using Balbharati 11th solutions Circle 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.

Get the free view of chapter 6 Circle 11th extra questions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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