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.

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.