Solve the problem.
-Find the equation of a circle with center at $( - 4,4 )$, passing through the point $( 2,12 )$. Write it in center-radius form.
A) $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 10$
B) $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 100$
C) $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 10$
D) $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$

Question

Quizplus · Accepted Answer

The equation of a circle in center-radius form is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. Given the center $(-4, 4)$, the equation becomes $(x + 4)^2 + (y - 4)^2 = r^2$. To find $r^2$, use the point $(2, 12)$ that lies on the circle: $(2 + 4)^2 + (12 - 4)^2 = 6^2 + 8^2 = 36 + 64 = 100$. Therefore, the equation is $(x + 4)^2 + (y - 4)^2 = 100$.

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