Question

If the circumference of the circle x² + y² + 8x + 8y – b = 0 is bisected by the circle x² + y² – 2x + 4y + a = 0 then a + b equal to

(a) 50

(b) 56

(c) –56

(d) –34

Answer 1

Correct option is (c) –56

Equation of radical axis (common chord of these circles) is

10x + 4y – b – a = 0

Centre of first circle is (–4, –4)

Since second circle bisects the first circle

Therefore centre of first circle must lie on common chord.

\(\therefore\) 10(–4) + 4(–4) – b – a = 0

–40 – 16 – (a + b) = 0

\(\therefore\) a + b = –56