Question

How do you find the center and radius of the circle with equation `(x - 2)^2 + (y + 5)^2 = 64`?

Answer 1

The equation of a circle with center `(0, 0)` and radius `r` is `(x-a)^2 + (y-b)^2 = r^2`. That means the center of this circle is `(2, -5)` and its radius is `sqrt64 = 8.`

Explanation:

The equation of a circle in standard form is:

`(x-a)^2+(y-b)^2=r^2`

The x-coordinate of the center is `a` the y-coordinate of the center is `b`, and `r` is the radius.

In this case, `a=2`, `b=-5` and `r=8`.