A circle has center (5,-4) and radius 8. Which gives the equation for the circle?

Use (x - h) ^2 + (x - k) ^2 = r^2.

Note: (h, k) is the center of the circle.

(h, k) = (5, - 4). This means h = 5 and k = - 4.

Let r = radius

We now plug and chug.

(x - 5) ^2 + (y - (-4)) ^2 = (8) ^2

(x - 5) ^2 + (y + 4) ^2 = 64

Done.