Answer
Center: $(-1,4)$ $;$ Radius: $5$
Domain: $[-6,4]$ $;$ Range: $[-1,9]$
The graph is:
Work Step by Step
$(x+1)^{2}+(y-4)^{2}=25$
The standard form of the equation of a circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$, where $(h,k)$ is the center of the circle and $r$ is its radius.
From the equation given, it can be seen that $(h,k)=(-1,4)$ and that $r^{2}=25$
The center of the circle is $(-1,4)$
The radius of the circle is:
$r^{2}=25$
$\sqrt{r^{2}}=\sqrt{25}$
$r=5$
From the equation's graph (shown below), it can be seen that its domain is $[-6,4]$ and its range is $[-1,9]$
