Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q II

HARD

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Find the equation of the circle which passes through the origin and intersects the circles, orthogonally: $x^{2} + y^{2} - 4 x - 6 y - 3 = 0, x^{2} + y^{2} - 8 y + 12 = 0$ .

Important Questions on System of Circle

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q II

Find the equation of the circle which passes through the point

(0, - 3)

and intersects the circles given by the equations

x^{2} + y^{2} - 6 x + 3 y + 5 = 0

and

x^{2} + y^{2} - x - 7 y = 0

orthogonally.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q II

Find the equation of the circle passing through the origin, having its center on the line

x + y = 4

and intersecting the circle

x^{2} + y^{2} - 4 x + 2 y + 4 = 0

orthogonally.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q II

Find the equation of the circle which passes through the points the circle

(2, 0), (0, 2)

and orthogonal to the circle

2 x^{2} + 2 y^{2} + 5 x - 6 y + 4 = 0

.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q II

Find the equation of the circle which cuts orthogonally the circle

x^{2} + y^{2} - 4 x + 2 y - 7 = 0

and having the center at

(2, 3)

.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q III

Find the equation of the circle which intersects the circle

x^{2} + y^{2} - 6 x + 4 y - 3 = 0

orthogonally and passes through the point

(3, 0)

and touches

Y -

axis.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q III

Find the equation of the circle which cuts the circles

x^{2} + y^{2} - 4 x - 6 y + 11 = 0

and

x^{2} + y^{2} - 10 x - 4 y + 21 = 0

orthogonally and has the diameter along the straight line

2 x + 3 y = 7

.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q III

If

P, Q

are conjugate points with respect to a circle

S \equiv x^{2} + y^{2} + 2 g x + 2 f y + c = 0

, then prove that the circle

P Q

as diameter cuts the circle

S = 0

orthogonally.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 2 - System of Circle>Exercise 2(a)>Q III

If the equations of two circles whose radii are

a, a^{'}

are

S = 0

and

S^{'} = 0

, then show that the circles

\frac{S}{a} + \frac{S^{'}}{a^{'}} = 0

and

\frac{S}{a} - \frac{S^{'}}{a^{'}} = 0

intersect orthogonally.