$$ x^2-20x+y^2-16y=-20 $$

The equation above defines a circle in the \(xy\)-plane. What is the radius of the circle?

Summary Submit Skip Question

We'll need to rewrite the equation into standard form:

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

In order to do this, we must complete the square as follows:

$$ x^2-20x+y^2-16y=-20 $$ $$ x^2-20x+\colorbox{aqua}{$100$} +y^2-16y=-20+\colorbox{aqua}{$100$} $$ $$ x^2-20x+100 +y^2-16y+\colorbox{yellow}{$64$}=-20+100+\colorbox{yellow}{$64$} $$ $$ \underbrace{x^2-20x+100}_\text{perfect square trinomial} + \underbrace{y^2-16y+64}_\text{perfect square trinomials} = -20+100+64 $$ $$ (x-10)^2+(y-8)^2=144 $$ $$ (x-10)^2+(y-8)^2=12^2$$ $$ r=\boxed{12} $$