Find an equation of the sphere with center $( 7 , - 5,7 )$ that touches the $x y$-plane.
A) $( x + 7 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 49$
B) $( x + 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 49$
C) $( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 40$
D) $( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 49$
E) $( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 7$

Question

Quizplus · Accepted Answer

The equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. The sphere touches the $xy$-plane when its radius is equal to the absolute value of its $z$-coordinate, which is $7$ in this case. Thus, $r = 7$, and the correct equation is $(x - 7)^2 + (y + 5)^2 + (z - 7)^2 = 49$.

Find an Equation of the Sphere with Center (7,−5,7)( 7 , - 5,7 )(7,−5,7)

Find an Equation of the Sphere with Center $( 7 , - 5,7 )$