What is the equation of a circle with a center located at (4,-1) and a radius of 9

The equation for a circle with the given information would be (x - 4) ^2 + (y + 1) ^2 = 81.

This is because the base form of a circle is:

(x - x1) ^2 + (y - y1) ^2 = r^2

In which, x1 is the x coordinate of the center and y1 is the y coordinate of the center. r is the radius of the circle. So we plug in to those and simplify.

(x - 4) ^2 + (y - - 1) ^2 = 9^2

(x - 4) ^2 + (y + 1) ^2 = 81