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 length of the diameter, which is $\frac{12-2}{2} = 5$. Therefore, the equation is $(x - 7)^2 + (y - 2)^2 = 5^2$, or $(x - 7)^2 + (y - 2)^2 = 25$.

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 $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$