1.2 – N – Analytical Geometry – II Exercise Problems

1.2 – N – Analytical Geometry – II Exercise Problems

Part – A

1.  Find the equation of the circle with centre (1, -2) and radius 5 units.

2.     Find the centre and radius of the circle  x2  +   y2 +  10x  +  8y  +  5 = 0 .

3.     Find the equation of the circle passing through the point (1 , 1 ) and concentric to the circle

x2  +   y2  +  4x  +  6y  –  15 = 0.

 Part – B

1.    Find the equation of the circle passing through the point  A (2, 3) and having its centre at C ( 4 , 1).

2.     Prove that the circles  x2  +   y2  – 8x  + 6y – 23 = 0  and x2  +   y2  – 2x  – 5y + 16 = 0 cut orthogonally .

Part – C

1.   Prove that the circles  x2  +   y2  – 4x  +  6y  + 8 = 0 and x2  +   y– 10x  –  6y  +14 = 0 touch each  other. 

2. Prove that the circles  x2  +   y2   – 2x  +  6y + 6= 0 and  x2  +   y2   – 5x  + 6y + 15 = 0 touch  each other.