The equation of the circle is
\((x+7)^{2}+(y+1)^{2}=r^{2}\)
for some radius \(r\).
We find \(r\) by plugging in the point \((8, 7)\):
\((8+7)^{2}+(7+1)^{2}=r^{2}\)
\(\rightarrow 15^{2}+8^{2}=r^{2}\)
\(\rightarrow 225+64=r^{2}\)
\(\rightarrow 289=r^{2}\)
\(\rightarrow r=17\)
So the radius is 17, and the equation is
\((x+7)^{2}+(y+1)^{2}=289\)
For the second part of the question, we plug in \(x=-15\):
\((-15+7)^{2}+(y+1)^{2}=289\)
\(\rightarrow (-8)^{2}+(y+1)^{2}=289\)
\(\rightarrow 64+(y+1)^{2}=289\)
\(\rightarrow (y+1)^{2}=225\)
\(\rightarrow y+1=\pm 15\)
\(\rightarrow y=14, -16\)
So the answer could either be 14 or -16.
