Find the center and radius of the circle with the given equation.
-$$x ^ { 2 } + 8 x + 16 + ( y + 9 ) ^ { 2 } = 81$$
A)Center (-4, -9), r = 9
B)Center (4, 9), r = 81
C)Center (-9, -4), r = 9
D)Center (9, 4), r = 81

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the standard form of a circle equation $(x - h)^2 + (y - k)^2 = r^2$ by completing the square for the x-terms. The equation $x^2 + 8x + 16$ is already a perfect square, $(x + 4)^2$, and $(y + 9)^2$ is also in the correct form. Thus, the center $(h, k)$ is $(-4, -9)$, and since the right side of the equation is $81$, the radius $r$ is the square root of $81$, which is $9$.

Find the Center and Radius of the Circle with the Given