x^2+8x+y^2-12y=-27

Question

Find the center as a coodinate
Find the radius

Answer 1

To find the center of the circle, we need to rewrite the given equation in the standard form of a circle equation, which is:

(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

First, complete the square for x^2 + 8x and y^2 - 12y:

x^2 + 8x + 16 + y^2 - 12y + 36 = -27 + 16 + 36
(x + 4)^2 + (y - 6)^2 = 25

Now, the equation is in the standard form. The center of the circle is (-4, 6) and the radius is √25 = 5.