Question

Let \(C_{1}\) and \(C_{2}\) are circle passing through (-9, 4 ), both are in contact with x + y = 3 and x - y = 3 (tangent lines). If \(r_{1}\) and \(r_{2}\) are radius of \(C_{1}\) and \(C_{2}\) respectively, then \(\left|r_{1}^{2}-r_{2}^{2}\right|\) equals to

(1) 400

(2) 768

(3) 625

(4) 250

Answer 1

Correct option is: (2) 768

\(\because \quad x+y=3\) and x - y = 3 are tangents

\(\therefore\) Both circle centre will lie on x-axis

\(\therefore (x-a)^{2}+y^{2}=r^{2}\)

Hence centre is C(a, 0)