Answer:
[tex](x+2)^{2}+y^{2}=64[/tex]
Step-by-step explanation:
The equation of a circle is given by [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex], where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
Substitute the points for [tex]h[/tex] and [tex]k[/tex] and simplify.
[tex](x-(-2))^{2}+(y-0)^{2}=r^2[/tex]
[tex](x+2)^2 + y^2 =r^2[/tex]
The diameter is given and the radius is half the length of the diameter, so the radius is 8
Substitute for [tex]r[/tex]
[tex](x+2)^2 +y^2 =8^2[/tex]
[tex](x+2)^2 +y^2 =64[/tex]
