Question

Find the center and radius of the circle whose equation is given by $x^2+y^2+4y=0$

Answer 1

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

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

Consider, $x^2+y^2+4y=0$, it can be rewritten as:

$x^2+y^2+4y+4=0+4$

implies $(x+0{)}^2+(y+2{)}^2=4$

So, comparing $(x+0{)}^2+(y+2{)}^2=4$ with the above equation of circle we get:

$h=0$, $k=-2$ and $r=2$

Therefore, center of the circle is $(0,-2)$ and radius of the circle is $r=2$.