MATH SOLVE

10 months ago

Q:
# 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?

Accepted Solution

A:

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.