Find the equation of a circle with center at $( - 6,2 )$, passing through the point $( - 3,6 )$. Write it in center-radius form.
A) $( x - 6 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$
B) $( x + 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$
C) $( x - 6 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 5$
D) $( x + 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The center-radius form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Given the center $(-6, 2)$, the equation becomes $(x + 6)^2 + (y - 2)^2 = r^2$. To find $r^2$, use the point $(-3, 6)$ that lies on the circle: $r^2 = (-3 + 6)^2 + (6 - 2)^2 = 3^2 + 4^2 = 9 + 16 = 25$. Thus, the correct equation is $(x + 6)^2 + (y - 2)^2 = 25$.

Find the Equation of a Circle with Center At (−6,2)( - 6,2 )(−6,2)

Find the Equation of a Circle with Center At $( - 6,2 )$