Answer
Circle
Work Step by Step
${{\left( x+2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=1$
The standard form of a circle is,
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$
Where $\left( h, k \right)$ is the center.
The provided equation ${{\left( x+2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=1$ resembles the standard equation of the circle
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$.
Thus, the provided equation ${{\left( x+2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=1$ is a circle.
Now to draw the graph, consider the provided equation,
${{\left( x+2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=1$
Now choose some values of x on both sides of the vertex and compute the corresponding y values.
$\begin{matrix}
x & y \\
-2 & 2 \\
-2 & 4 \\
-1 & 3 \\
-3 & 3 \\
\end{matrix}$
Next, we graph.
