Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$.
A) $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$
B) $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$
C) $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$
D) $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left( \frac{-5 + 3}{2}, \frac{1 + 7}{2} \right) = (-1, 4)$. The radius is half the distance between the endpoints, calculated using the distance formula: $\sqrt{(3 - (-5))^2 + (7 - 1)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$. The radius is half of this, so $r = 5$. Thus, the equation is $(x + 1)^2 + (y - 4)^2 = 25$.

Find the Center-Radius Form of the Equation of the Circle (−5,1)( - 5,1 )(−5,1)

Find the Center-Radius Form of the Equation of the Circle $( - 5,1 )$