Write the equation for the shape described.
-The circle with center at $( - 6 , - 2 )$, passing through $( - 3,2 )$
A) $( x - 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$
B) $( x + 2 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 9$
C) $( x - 2 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 9$
D) $( x + 6 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. The center is given as $(-6, -2)$, so $h = -6$ and $k = -2$, which matches the form in option D. To find the radius, calculate the distance between the center $(-6, -2)$ and a point on the circle $(-3, 2)$. The distance (or radius) squared is $((-3) - (-6))^2 + (2 - (-2))^2 = 3^2 + 4^2 = 9 + 16 = 25$, which matches the radius squared in option D.

Write the Equation for the Shape Described (−6,−2)( - 6 , - 2 )(−6,−2)

Write the Equation for the Shape Described $( - 6 , - 2 )$