Write the standard form of the equation of the circle.
-The endpoints of a diameter are (3, 6)and (7, 6).
A) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$
B) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 4$
C) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 2$
D) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2$

Question

Write the standard form of the equation of the circle.
-The endpoints of a diameter are (3, 6)and (7, 6). 
A) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$
B) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 4$
C) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 2$
D) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2$

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left(\frac{3+7}{2}, \frac{6+6}{2}\right) = (5, 6)$. The radius is half the distance between the endpoints of the diameter, which is $\frac{7-3}{2} = 2$. Thus, the equation is $(x - 5)^2 + (y - 6)^2 = 2^2 = 4$.

Write the Standard Form of the Equation of the Circle (x−5)2+(y−6)2=4( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4(x−5)2+(y−6)2=4

Write the Standard Form of the Equation of the Circle $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$