Write an equation for a circle with
a center at (9 -2) and has a
radius of 7.

The equation of a circle is given as:

(x-a)^2 + (y- b)^2 = r^2  where (a, b) is the center.

(x-9)^2  = x^2 -18x + 81 - (i)
(y+2)^2 =y^2 + 4y +4       (ii)
r^2 = 49                           (iii)

Adding equation (i) and (iii) 
x^2 + y^2 - 18x + 4y + 85 (iv)

Equating equation (iv) and (iii)

 x^2 + y^2 - 18x + 4y + 85 = 49

Arrange the equation:

 x^2 + y^2 - 18x + 4y + 36 = 0

I hope this helps