Find the center and radius of the circle whose equation is 5x^2−6x+5y^2+8y−9=0.

We need to rearrange terms into the standard equation:

5x^2−6x+5y^2+8y−9=0
5(x^2 - 6/5 x) + 5(y^2 + 8/5 y) = 9
(x^2 - 6/5 x + 9/25) + (y^2 + 8/5 y + 16/25) = 9/5 + 9/25 + 16/25
(x - 3/5)^2 + (y + 4/5)^2 = 70/25

Now you can read off the desired data.