Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter:
$( - 7,4 ) , ( 1,6 )$
A) $( x + 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 17$
B) $( x - 5 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 17$
C) $( x - 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 17$
D) $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 125$
E) $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 125$

Question

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: 
$( - 7,4 ) , ( 1,6 )$ 
A) $( x + 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 17$
B) $( x - 5 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 17$
C) $( x - 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 17$
D) $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 125$
E) $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 125$

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left( \frac{-7 + 1}{2}, \frac{4 + 6}{2} \right) = (-3, 5)$. The radius can be found using the distance formula between one endpoint and the center, which gives $r = \sqrt{(-7 + 3)^2 + (4 - 5)^2} = \sqrt{16 + 1} = \sqrt{17}$. Thus, the equation is $(x + 3)^2 + (y - 5)^2 = 17$.

Write the Standard Form of the Equation of the Circle (−7,4),(1,6)( - 7,4 ) , ( 1,6 )(−7,4),(1,6)

Write the Standard Form of the Equation of the Circle $( - 7,4 ) , ( 1,6 )$