Write the equation for the shape described.
-The circle with endpoints of a diameter at $( 2,9 )$ and $( 6,1 )$
A) $( x - 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 20$
B) $( x - 4 ) ^ { 2 } + y ^ { 2 } = 16$
C) $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 20$
D) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 4$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left( \frac{2+6}{2}, \frac{9+1}{2} \right) = (4, 5)$. The radius can be found using the distance formula between the center and one of the endpoints, resulting in $\sqrt{(6-4)^2 + (1-5)^2} = \sqrt{4+16} = \sqrt{20}$. Thus, the equation is $(x-4)^2 + (y-5)^2 = 20$.

Write the Equation for the Shape Described (2,9)( 2,9 )(2,9) And (6,1)( 6,1 )(6,1)

Write the Equation for the Shape Described $( 2,9 )$ And $( 6,1 )$