Find the standard form of the equation of the sphere with the given characteristics.
Center: $( 7,0 , - 14 )$ ;diameter: 14

A) $( x + 7 ) ^ { 2 } + y ^ { 2 } + ( z + 14 ) ^ { 2 } = 49$
B) $( x - 7 ) ^ { 2 } + y ^ { 2 } + ( z + 14 ) ^ { 2 } = 49$
C) $( x - 7 ) ^ { 2 } - y ^ { 2 } - ( z - 14 ) ^ { 2 } = 49$
D) $( x - 7 ) ^ { 2 } + y ^ { 2 } + ( z - 14 ) ^ { 2 } = 49$
E) $( x + 7 ) ^ { 2 } - y ^ { 2 } - ( z + 14 ) ^ { 2 } = 49$

Question

Find the standard form of the equation of the sphere with the given characteristics. 
Center: $( 7,0 , - 14 )$ ;diameter: 14

A) $( x + 7 ) ^ { 2 } + y ^ { 2 } + ( z + 14 ) ^ { 2 } = 49$
B) $( x - 7 ) ^ { 2 } + y ^ { 2 } + ( z + 14 ) ^ { 2 } = 49$
C) $( x - 7 ) ^ { 2 } - y ^ { 2 } - ( z - 14 ) ^ { 2 } = 49$
D) $( x - 7 ) ^ { 2 } + y ^ { 2 } + ( z - 14 ) ^ { 2 } = 49$
E) $( x + 7 ) ^ { 2 } - y ^ { 2 } - ( z + 14 ) ^ { 2 } = 49$

Quizplus · Accepted Answer

The standard form of the equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. Given the center $(7, 0, -14)$ and diameter $14$, the radius is $14/2 = 7$. Thus, the equation is $(x - 7)^2 + (y - 0)^2 + (z + 14)^2 = 7^2$, which simplifies to $(x - 7)^2 + y^2 + (z + 14)^2 = 49$.

Find the Standard Form of the Equation of the Sphere (7,0,−14)( 7,0 , - 14 )(7,0,−14)

Find the Standard Form of the Equation of the Sphere $( 7,0 , - 14 )$