Answer
A circle with center at $C(-2,2)$ and radius $2$.
.
Work Step by Step
Gather terms containing x and y in separate parentheses
$(x^{2}+4x)+(y^{2}-4y)=-4$
Complete squares:
$x^{2}+4x=x^{2}+2\cdot x\cdot 2+2^{2}-2^{2}=(x+2)^{2}-4$
$y^{2}-4y=y^{2}-2\cdot y\cdot 2+2^{2}-2^{2}=(y-2)^{2}-4$
The equation becomes
$(x+2)^{2}-4+(y-2)^{2}-4=-4$
$(x+2)^{2}+(y-2)^{2}=4$
A circle with center at $C(-2,2)$ and radius $2$
x-intercepts $:\quad\left[\begin{array}{l}
(x+2)^{2}+(0-2)^{2}=4\\
(x+2)^{2}+4=4\\
x=-2\\
(-2,0)
\end{array}\right]$,
y-intercepts $:\quad\left[\begin{array}{l}
(0+2)^{2}+(y-2)^{2}=4\\
4+(y-2)^{2}=4\\
y=2\\
(0,2)
\end{array}\right]$
