Find the center-radius form of the circle described or graphed.
-Find the center-radius form of the equation of a circle with center $( 5,7 )$ and tangent to the $x$-axis.
A) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 49$
B) $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$
C) $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 49$
D) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The center-radius form of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Given the center $(5, 7)$ and that the circle is tangent to the $x$-axis, the distance from the center to the $x$-axis (7 units) is the radius. Thus, $r = 7$, and the equation is $(x - 5)^2 + (y - 7)^2 = 49$.

Find the Center-Radius Form of the Circle Described or Graphed (5,7)( 5,7 )(5,7)

Find the Center-Radius Form of the Circle Described or Graphed $( 5,7 )$