How do i write a equation of 8x+x^2-2y=64-y^2 ?

Answer 1

I recognize this to be an circle.

Do you want it in standard form?

if so, then ...
8x+x^2-2y=64-y^2
x^2 + 8x + ... + y^2 - 2y + ... = 64
complete the square

x^2 + 8x + 16 + y^2 - 2y + 1 = 64 + 16 + 1
(x + 4)^2 + (y-1)^2 = 81

centre is (-4,1), radius is 9