Question

Find the center and radius of the circle whose equation is given by ${(x-2)}^2+{(y+5)}^2=13$

Answer 1

An equation of the circle with center $(h,k)$ and radius $r$ is

$(x-h{)}^2+(y-k{)}^2=r^2$

So, comparing $(x-2{)}^2+(y+5{)}^2=13$ that is $(x-2{)}^2+(y-\left(5\right){)}^2=13$ with the above equation of circle we get:

$h=2$, $k=-5$ and $r=\sqrt{13}$

Therefore, center of the circle is $(2,-5)$ and radius of the circle is $r=\sqrt{13}$.