Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 2,3 )$ and $( 8 , - 5 )$
A) $x ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$
B) $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 41$
C) $( x - 3 ) ^ { 2 } + y ^ { 2 } = 16$
D) $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 41$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, calculated as $(\frac{-2+8}{2}, \frac{3-5}{2}) = (3, -1)$. The radius is half the distance between the endpoints, calculated as $\sqrt{(8 - (-2))^2 + (-5 - 3)^2} / 2 = \sqrt{100 + 64} / 2 = \sqrt{164} / 2 = \sqrt{41}$. Thus, the equation is $(x - 3)^2 + (y + 1)^2 = 41$.

Find the Center-Radius Form of the Circle Described or Graphed (−2,3)( - 2,3 )(−2,3)

Find the Center-Radius Form of the Circle Described or Graphed $( - 2,3 )$