Use the given information about a circle to write an equation of the circle in standard form.
-The endpoints of a diameter are $( 3,11 )$ and $( - 9 , - 5 )$.
A) $( x - 3 ) ^ { 2 } + ( y - 11 ) ^ { 2 } = 100$
B) $( x + 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 100$
C) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 20$
D) $( x + 3 ) ^ { 2 } + ( y + 11 ) ^ { 2 } = 20$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is calculated as $\left( \frac{3 + (-9)}{2}, \frac{11 + (-5)}{2} \right) = (-3, 3)$. The radius can be found by the distance formula between one endpoint and the center, which gives $r = \sqrt{(3 + 3)^2 + (11 - 3)^2} = 10$. Thus, the equation is $(x + 3)^2 + (y - 3)^2 = 100$.

Use the Given Information About a Circle to Write an Equation