Answer
multiple answers; see details
Work Step by Step
The standard form of the equation $
4x^2+4y^2+16x+8y=1
$ is
\begin{array}{l}
x^2+y^2+4x+2y=\dfrac{1}{4}\text{... divide both sides by $4$}\\\\
(x^2+4x)+(y^2+2y)=\dfrac{1}{4}\\\\
(x^2+4x+4)+(y^2+2y+1)=\dfrac{1}{4}+4+1\\\\
(x+2)^2+(y+1)^2=\dfrac{21}{4}
.\end{array}
The graph of this equation is a $\text{
circle
}$ with the following properties:
\begin{array}{l}
\text{Center: }\left(
-2,-1
\right),\\\\\text{Radius: }
\dfrac{\sqrt{21}}{2}
.\end{array}
Using the properties above, the graph of the equation is given below.
