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) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 49$
C) $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$
D) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Question

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) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 49$
C) $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$
D) $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

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 the fact 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 becomes $(x - 5)^2 + (y - 7)^2 = 49$.

Find the Center-Radius Form of the Equation of a Circle (x+5)2+(y+7)2=49( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 49(x+5)2+(y+7)2=49

Find the Center-Radius Form of the Equation of a Circle $( x + 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 49$