Question

Find the center and radius of the circle whose equation is given by $x^2+y^2+6x-10y=9$

Answer 1

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

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

Consider, $x^2+y^2+6x-10y=9$, it can be rewritten as:

$x^2+y^2+6x-10y+9+25=9+9+25$

implies $(x+3{)}^2+(y-5{)}^2=43$

So, comparing $(x+3{)}^2+(y-5{)}^2=43$ with the above equation of circle, we get:

$h=-3$, $k=5$ and $r=\sqrt{43}$

Therefore, center of the circle is $(-3,5)$ and radius of the circle is $r=\sqrt{43}$.