An equation of a circlewith radius r and center (h,k) is in form
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Diameter is twice radius so find the distance between the given points and halve it to get radius
D=[tex] \sqrt{( x_{1}-x_{2})^2+(y_{1}-y_{2})^2}[/tex]
D=[tex] \sqrt{( 8-(-4))^2+(-9-(-7))^2}[/tex]
D=[tex] \sqrt{144+4}[/tex]
D=√148
D=2√37
Halve that
R=√37
The center is the midpoint of the 2 points that make up the diameter
So find the midpoint of the points (8,-9) and (-4,-7)
Midpoint of two points (x1,y1) and (x2,y2) is [tex]( \frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Midpoint between (8,-9) and (-4,-7) is (2,-8)
That is the center of the circle (h,k)
so
R=√37
(h,k)=(2,-8)
So the equation is
[tex](x-2)^2+(y+8)^2=37[/tex]
