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 (c) –56

Explanation:

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.

10( – 4) + 4( – 4) – b – a = 0

– 40 – 16 – (a + b) = 0

a + b = – 56