Consider the circles and

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider the circles

S_1: x^2 + y^2 - 4x - 6y + 12 = 0

and

S_2: (x - 5)^2 + (y - 6)^2 = r^2 > 1

Column I	Column II
(A) $S_1$ and $S_2$ touch internally, then $(r - 1)^2$ is divisible by	(p)	3
(B) $S_1$ and $S_2$ touch externally, then $r^2 + 2r + 3$ is divisible by	(q)	4
(C) $S_1$ and $S_2$ intersect orthogonally, then $r^2 - 1$ is divisible by	(r)	5
(D) $S_1$ and $S_2$ intersect so that the common chord is longest, then $r^2 + 5$ is divisible by	(s)	6