Answer
Circle
Work Step by Step
$\begin{align}
& {{x}^{2}}+{{y}^{2}}-8y-20=0 \\
& {{x}^{2}}+{{y}^{2}}-8y=20
\end{align}$
Add $16$ on both sides of the equation,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}-8y+16=20+16 \\
& {{x}^{2}}+{{y}^{2}}-2\left( 4y \right)+{{4}^{2}}=36 \\
& {{x}^{2}}+{{\left( y-4 \right)}^{2}}={{6}^{2}}
\end{align}$
Consider the standard form of the circle,
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$
Where $\left( h, k \right)$ is the center.
The simplified equation ${{x}^{2}}+{{\left( y-4 \right)}^{2}}={{6}^{2}}$ resembles the equation of the circle.
Thus, the equation ${{x}^{2}}+{{y}^{2}}-8y-20=0$ is a circle.
Now to draw the graph, consider the provided equation,
${{x}^{2}}+{{y}^{2}}-8y-20=0$
Now choose some values of x and compute the corresponding y values.
$\begin{matrix}
x & y \\
0 & -2 \\
0 & 10 \\
6 & 4 \\
-6 & 4 \\
\end{matrix}$
Next, plot the points.
