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

HARD

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Find the equation and length of the common chord of the following circles: $x^{2} + y^{2} + 2 x + 2 y + 1 = 0, x^{2} + y^{2} + 4 x + 3 y + 2 = 0$ .

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(b)>Q III

Find the equation and length of the common chord of the following circles:

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

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Prove that the radical axis of the circles

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

and

x^{2} + y^{2} + 2 g^{'} x + 2 f^{'} y + c^{'} = 0

is the diameter of the latter circle (or the former bisects the circumference of the latter) if

2 g^{'} (g - g^{'}) + 2 f^{'} (f - f^{'}) = c - c^{'}

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Show that the circles

x^{2} + y^{2} + 2 a x + c = 0

and

x^{2} + y^{2} + 2 b y + c = 0

touch each other if

\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{c}

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Show that the circles

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

and

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

touch each other. Find the coordinates of the point of contact. Is the point of contact external or internal?

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Find the equation of the circle which cuts the following circles orthogonally:

x^{2} + y^{2} + 4 x - 7 = 0, 2 x^{2} + 2 y^{2} + 3 x + 5 y - 9 = 0, x^{2} + y^{2} + y = 0

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Find the equation of the circle which cuts the following circles orthogonally:

x^{2} + y^{2} + 2 x + 4 y + 1 = 0, 2 x^{2} + 2 y^{2} + 6 x + 8 y - 3 = 0, x^{2} + y^{2} - 2 x + 6 y - 3 = 0

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Find the equation of the circle which cuts the following circles orthogonally:

x^{2} + y^{2} + 2 x + 17 y + 4 = 0, x^{2} + y^{2} + 7 x + 6 y + 11 = 0, x^{2} + y^{2} - x + 22 y + 3 = 0

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

Find the equation of the circle which cuts the following circles orthogonally:

x^{2} + y^{2} + 4 x + 2 y + 1 = 0, 2 (x^{2} + y^{2}) + 8 x + 6 y - 3 = 0, x^{2} + y^{2} + 6 x - 2 y - 3 = 0

.