If the circles and intersect in two distinct points and

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the circles

x^2 + y^2 + 2ax + cy + a = 0

and

x^2 + y^2 - 3ax + dy - 1 = 0

intersect in two distinct points

P

and

Q

, then the line

5x + by - a = 0

passes through

P

and

Q

. (1) exactly one value of

a

(2) no value of

a

(3) infinitely many values of

a

(4) exactly two values of

a