Question

If the circles ax2 + ay2 + 2bx + 2cy = 0 and

Ax2 + Ay2 + 2Bx + 2Cy = 0 touch each other, then-

• A. bC = Cb
• B. aC = cA
• C. aB = bA
• D. $\frac{a}{A} = \frac{b}{B} = \frac{c}{C}$

Answer 1

Answer: (A)

bC = Cb

Answer 2

Obviously both circles, pass through the origin and therefore O must be the point of contact.

\ centres P, Q, O are collinear.

$\left( –\frac{b}{a},–\frac{c}{a} \right)$, (0, 0) and $\left( –\frac{B}{A},–\frac{C}{A} \right)$are collinear

\ $\frac{c}{b} = \frac{C}{B}$ or cB = Bc