Find the center-radius form of the circle described or graphed.
-Find the equation of a circle with center at $( - 4,4 )$, passing through the point $( - 1,8 )$. Write it in center-radius form.
A) $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 5$
B) $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$
C) $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 25$
D) $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The center-radius form of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Given the center $(-4, 4)$, the equation becomes $(x + 4)^2 + (y - 4)^2 = r^2$. To find $r^2$, calculate the distance between the center $(-4, 4)$ and the point $(-1, 8)$ using the distance formula: $r^2 = (-1 + 4)^2 + (8 - 4)^2 = 3^2 + 4^2 = 9 + 16 = 25$. Therefore, the equation is $(x + 4)^2 + (y - 4)^2 = 25$.

Find the Center-Radius Form of the Circle Described or Graphed (−4,4)( - 4,4 )(−4,4)

Find the Center-Radius Form of the Circle Described or Graphed $( - 4,4 )$