Find the center and radius of the circle with the given equation.
-$$x ^ { 2 } - 12 x + 36 + y ^ { 2 } - 8 y + 16 = 4$$
A) Center $( 6,4 ) , r = 2$
B) Center $( - 4 , - 6 ) , r = 4$
C) Center $( 4,6 ) , \mathrm { r } = 2$
D) Center $( - 6 , - 4 ) , \mathrm { r } = 4$

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 - 12x + 36 + y^2 - 8y + 16 = 4$, we complete the squares for $x$ and $y$. The equation is already arranged in a way that makes completing the square straightforward. For $x^2 - 12x + 36$, we see that it forms a perfect square $(x-6)^2$, and for $y^2 - 8y + 16$, it forms $(y-4)^2$. Thus, the equation can be rewritten as $(x-6)^2 + (y-4)^2 = 4$. This shows that the center of the circle is $(6, 4)$ and the radius $r$ is the square root of $4$, which is $2$.

Find the Center and Radius of the Circle with the Given