Problem. If the circles $\large x^2 + y^2 + 2ax + b = 0 $ and $\large x^2 + y^2 + 2cx + b = 0 $touch each other, then
(A) b > 0
(B) b < 0
(C) b = 0
(D) none of these
Sol. Since the circles touch each other, equation of the common tangent is S1– S2= 0
⇒ x = 0.
Putting x = 0 in the equations of the circles, we get y2+ b = 0.
This equation should have equal roots ⇒ b = 0.
Hence (C) is the correct answer.