Find the standard form of the equation of the sphere with the given characteristics.
Center: $( 5,0 , - 6 )$ ;radius: 6

A) $( x - 5 ) ^ { 2 } - y ^ { 2 } + ( z + 6 ) ^ { 2 } = 36$
B) $( x - 5 ) ^ { 2 } - y ^ { 2 } - ( z + 6 ) ^ { 2 } = 36$
C) $( x - 5 ) ^ { 2 } + y ^ { 2 } + ( z + 6 ) ^ { 2 } = 36$
D) $( x - 5 ) ^ { 2 } + y ^ { 2 } + ( z - 6 ) ^ { 2 } = 36$
E) $( x - 5 ) ^ { 2 } - y ^ { 2 } - ( z - 6 ) ^ { 2 } = 36$

Question

Find the standard form of the equation of the sphere with the given characteristics. 
Center: $( 5,0 , - 6 )$ ;radius: 6

A) $( x - 5 ) ^ { 2 } - y ^ { 2 } + ( z + 6 ) ^ { 2 } = 36$
B) $( x - 5 ) ^ { 2 } - y ^ { 2 } - ( z + 6 ) ^ { 2 } = 36$
C) $( x - 5 ) ^ { 2 } + y ^ { 2 } + ( z + 6 ) ^ { 2 } = 36$
D) $( x - 5 ) ^ { 2 } + y ^ { 2 } + ( z - 6 ) ^ { 2 } = 36$
E) $( x - 5 ) ^ { 2 } - y ^ { 2 } - ( z - 6 ) ^ { 2 } = 36$

Quizplus · Accepted Answer

The standard form of the equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. For a sphere with center $(5, 0, -6)$ and radius $6$, the equation is $(x - 5)^2 + (y - 0)^2 + (z + 6)^2 = 6^2$, which simplifies to $(x - 5)^2 + y^2 + (z + 6)^2 = 36$.

Find the Standard Form of the Equation of the Sphere (5,0,−6)( 5,0 , - 6 )(5,0,−6)

Find the Standard Form of the Equation of the Sphere $( 5,0 , - 6 )$