Question

at is the center and radius of x^2+y^2+8x+8y=17

Answer 1

Have you considered "completing the square?" That's the standard method used when you wish to determine the center and radius of a circle whose equation is not given in std. form.

Rewrite x^2+y^2+8x+8y=17 as x^2 + 8x + y^2 + 8y = 17
and complete the square for each variable, separately.