Question

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

Answer 1

Radius will be:

$\left|\frac{5.3-12.4-12}{\sqrt{5^2+{12}^2}}\right|=\frac{45}{13}$.

So the equation of the circle will be,

$(x-3{)}^2+(y+4{)}^2={\left(\frac{45}{13}\right)}^2$.