Find the center (h, k) and radius r of the circle with the given equation.
-$$x ^ { 2 } - 16 x + 64 + ( y + 3 ) ^ { 2 } = 9$$
A) $( h , k ) = ( 8 , - 3 ) ; r = 3$
B) $( h , k ) = ( - 8,3 ) ; r = 9$
C) $( \mathrm { h } , \mathrm { k } ) = ( - 3,8 ) ; \mathrm { r } = 3$
D) $( h , k ) = ( 3 , - 8 ) ; r = 9$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form $(x - h)^2 + (y - k)^2 = r^2$ by completing the square for the $x$ terms. Completing the square for $x^2 - 16x + 64$ gives $(x - 8)^2$, since $(-8)^2 = 64$. The equation already has $(y + 3)^2$ which is in the desired form. Thus, the center $(h, k) = (8, -3)$ and the radius $r = 3$, because the equation matches the form $(x - 8)^2 + (y + 3)^2 = 3^2$.

Find the Center (H, K) and Radius R of the Circle