find the center and radius of the circle with the equation:x squared +16x+64+y squared-2y + 1=144

To find the center and radius of the circle from the given equation, we need to rewrite the equation in standard form, which is (x-h)^2 + (y-k)^2 = r^2 , where (h, k) is the center of the circle, and r is the radius.

Given equation: x^2 + 16x + 64 + y^2 - 2y + 1 = 144

First, complete the square for x terms:
x^2 + 16x + 64 = (x + 8)^2

Next, complete the square for y terms:
y^2 - 2y + 1 = (y - 1)^2

Now rewrite the given equation in standard form:
(x + 8)^2 + (y - 1)^2 = 144

Comparing with the standard form: (x - h)^2 + (y - k)^2 = r^2 , we have:
Center: (h, k) = (-8, 1)
Radius: r = \sqrt{144} = 12

\textbf{Answer:} The center of the circle is (-8, 1) and the radius is 12 .