Draw a picture. The center of the circle is at (h,k), and (9,2) lies on the circle.
Since the circle is tangent to both the x- and the y-axes, h=r and k=r.
The distance from the center (r,r) to the point (9,2) is
d = r = sqrt( (r-9)^2 + (r-2)^2 ), or r^2 = (r-9)^2 + (r-2)^2
or r^2 = r^2 - 18r + 81 + r^2 - 4r + 4
Simpifying, r^2 = 2r^2 - 22r + 85, or r^2 - 22r + 84 = 0.
This quadratic can be solved using the quadratic formula or some other approach. The roots are 5 and 17.
Thus, the center of the circle is (5,5) and the radius is 5.
The equation of the circle is then (x-5)^2 + (y-5)^2 = 5^2.
Check: does (9,2) satisfy this equation? (9-5)^2 + (2-5)^2 = 25
4^2 + 3^2 = 25 is TRUE.
You must now go thru the same procedure with r = 17. Is
(x-9)^2 + (y-2)^2 = 25 when the center is (17,17)?
