The equation of the circle having centre at $(3,-4)$ and touching the line $5x+12y-12=0$ is __________

Question

[Hint : To determine radius find the perpendicular distance from the centre of the circle to the line.]

$\begin{array}{1 1}(x-3)^2+(y+4)^2=45^2\\(x-3)^2+(y+4)^2=\large\frac{\sqrt{45}}{13}\\(x-3)^2+(y+4)^2=\big(\large\frac{45}{13}\big)^2\\(x-3)^2+(y+4)^2=\sqrt{\large\frac{45}{13}}\end{array}$