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