The equation of a circle is x2+8x+y2-12y=144. What are the coordinates of the center and the length of the radius of the circle?

To find the center and radius of the circle from its equation in standard form, we need to complete the square for both the x and y terms. This will allow us to write the equation in the form: (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center of the circle and r is the radius. So let's begin by completing the square for the x terms: x^2 + 8x + y^2 - 12y = 144 (x^2 + 8x + 16) + (y^2 - 12y + 36) = 144 + 16 + 36 (x + 4)^2 + (y - 6)^2 = 196 Now we have the equation in the desired form, and we can read off the center and radius: Center = (-4, 6) Radius = sqrt(196) = 14 Therefore, the center of the circle is (-4, 6) and the radius is 14.