Write the equation for the shape described.
-The circle with endpoints of a diameter at $( 3 , - 5 )$ and $( 7 , - 4 )$
A) $( x + 2 ) ^ { 2 } + \left( y + \frac { 1 } { 2 } \right) ^ { 2 } = 17$
B) $( x + 5 ) ^ { 2 } + \left( y + \frac { 9 } { 2 } \right) ^ { 2 } = 101$
C) $( x + 5 ) ^ { 2 } + \left( y - \frac { 9 } { 2 } \right) ^ { 2 } = 181$
D) $( x - 5 ) ^ { 2 } + \left( y + \frac { 9 } { 2 } \right) ^ { 2 } = \frac { 17 } { 4 }$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, calculated as $(\frac{3+7}{2}, \frac{-5-4}{2}) = (5, -\frac{9}{2})$. The radius is half the distance between the endpoints, calculated as $\sqrt{(7-3)^2 + (-4+5)^2}/2 = \sqrt{17}/2$. The equation is $(x-5)^2 + (y+\frac{9}{2})^2 = (\frac{\sqrt{17}}{2})^2 = \frac{17}{4}$.

Write the Equation for the Shape Described (3,−5)( 3 , - 5 )(3,−5)

Write the Equation for the Shape Described $( 3 , - 5 )$