Find the center and radius of the circle $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25$ .
A)center: (1, 5), radius 5
B)center: (5, 1), radius 25
C)center: (-5, -1), radius 5
D)center: (-5, -1), radius 25
E)center: (5, 1), radius 5

Question

Quizplus · Accepted Answer

The equation of a circle in the form $(x - h)^2 + (y - k)^2 = r^2$ has a center at $(h, k)$ and a radius of $r$. For the given equation, $h = 5$, $k = 1$, and $r^2 = 25$, so $r = 5$. Therefore, the center is $(5, 1)$ and the radius is $5$.

Find the Center and Radius of the Circle (x−5)2+(y−1)2=25( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25(x−5)2+(y−1)2=25

Find the Center and Radius of the Circle $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25$