Find the center and radius of the circle with equation x2 + y2 − 18x + 12y + 81 = 0.center     (x, y) = (No Response) radius

The equation of a circle is typically given in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

The given equation is x² + y² - 18x + 12y + 81 = 0.

To find the center and the radius, we need to rewrite this equation in the standard form.

First, group the x terms and the y terms:

(x² - 18x) + (y² + 12y) = -81

To complete the square, we take half of the coefficient of x, square it and add it to both sides. We do the same for y.

Half of -18 is -9, and (-9)² = 81.

Half of 12 is 6, and 6² = 36.

So, add these to both sides:

(x² - 18x + 81) + (y² + 12y + 36) = -81 + 81 + 36

This simplifies to:

(x - 9)² + (y + 6)² = 36

So, the center of the circle (h, k) is (9, -6) and the radius r is the square root of 36, which is 6.