Write the standard form of the equation of the circle with the given characteristics.
Endpoints of a diameter: (2,2), (12,2)

A) $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$
B) $( x - 2 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$
C) $( x + 2 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$
D) $( x + 7 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$
E) $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$

Question

Write the standard form of the equation of the circle with the given characteristics. 
Endpoints of a diameter: (2,2), (12,2)

A) $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$
B) $( x - 2 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
C) $( x + 2 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$ 
D) $( x + 7 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$ 
E) $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left(\frac{2+12}{2}, \frac{2+2}{2}\right) = (7, 2)$. The radius is half the distance between the endpoints of the diameter, which is $\frac{\sqrt{(12-2)^2 + (2-2)^2}}{2} = \frac{\sqrt{100}}{2} = 5$. Thus, the equation is $(x - 7)^2 + (y - 2)^2 = 5^2 = 25$.

Write the Standard Form of the Equation of the Circle (x−7)2+(y−2)2=5( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5(x−7)2+(y−2)2=5

Write the Standard Form of the Equation of the Circle $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$