Question

The equation of the line of centres of the system of co-axal circles x² + y² + 2ax + 2by + c + 2λ (ax – by + 1) = 0 is-

• A. ax –by + 1 = 0
• B. bx + ay + ab = 0
• C. bx + ay + 2ab = 0
• D. bx + ay + $\sqrt{a^{2} + b^{2}}$= 0

Answer 1

Answer: (C)

bx + ay + 2ab = 0

Answer 2

The line of centres will be perpendicular to radical axis, so its equation is bx + ay + k = 0

It must pass through the centre (–a, –b) of the member of the system, so, k = 2ab

Hence the desired equation is bx + ay + 2ab = 0