Consider points $A(\sqrt{13},0)$ and $B(2\sqrt{13},0)$ lying on x-axis. These points are rotated in anticlockwise direction about the origin through an angle of ${\tan }^{-1}\left(\frac{2}{3}\right)$ . Let the new position of A and B be $A\text{'}andB\text{'}$ , respectively. With $A\text{'}$as centre and radius $\frac{2\sqrt{13}}{3}$ , a circle  $C_1$  is drawn and with $B\text{'}$ as centre and radius $\frac{\sqrt{13}}{3}$ , a circle $C_2$ is drawn. The radical axis of  $C_{1}and{C}_2$ is  $\mathcal{l}x+my=65$