Question

Find the center and radius for the circle with the equation 4(x-5)^2=4y^2=64

Answer 1

Do you mean:
\( 4(x - 5)^2 \color{red}{+} 4y^2 = 64 \) ?
If so, we could use the standard form of the circle by dividing both sides by 4. \((x -h)^2 + (y -k)^2 = r^2 \)