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COLUMN - I COLUMN - II
(A) The circle $x^{2} + y^{2} + 2 x + c = 0$ and $x^{2} + y^{2} + 2 y + c = 0$ touch each other (p) if c = 1
(B) The circle $x^{2} + y^{2} + 2 x + 3 y + c^{2} = 0$ and $x^{2} + y^{2} - x + 2 y + c^{2} = 0$ intersect orthogonally (q) if c = –1
(C) The circle $x^{2} + y^{2} = 9$ contains the circle $x^{2} + y^{2} - 2 x + 1 - c^{2} = 0$ (r) if c = 1/2
(D) The circle $x^{2} + y^{2} = 9$ is contained in the circle $x^{2} + y^{2} - 6 x - 8 y + 25 - c^{2} = 0$ (s) if c > 8
A B C D
1) r p,q p,q,r s
2) q,p r p,q,r r
3) p,q,r r r q,p
4) r r q,p p,q,r

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answer is A.

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Detailed Solution

A) $c_{1} c_{2} = r_{1} + r_{2}$

B) The circle intersect orthogonally if $2 (1) (- 1 / 2) + 2 (3 / 2) = c^{2} + c^{2} {or if c}^{2} = 1$

C) $c_{1} c_{2} < |r_{1} - r_{2}| \Rightarrow - 2 < 0 < 2$

D) $c_{1} c_{2} < |r_{1} - r_{2}| \Rightarrow | c | > 8$

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