Question

Determine and state the coordinates of the center and length of the radius of a circle whose equation is
$x^{2} + y ^{2} - 6x = 56 - 8y$
Please explain how to do this.

Answer 1

First, rewrite the equation in standard form.
The center-radius form of the circle equation is in the format:
(x – h)^2 + (y – k)^2 = r^2
with the center being at the point (h, k) and the radius being "r".

(x-3)^2 + (y+4)^2 = 81

From here, you can determine the center and radius. The center is at (3,-4) and the radius is 9.