Find the standard form of the equation of the sphere with the given characteristics.
Center: $( 4,3,5 )$ ;radius: 5

A) $( x - 4 ) ^ { 2 } - ( y + 3 ) ^ { 2 } - ( z - 5 ) ^ { 2 } = 25$
B) $( x - 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
C) $( x + 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
D) $( x - 4 ) ^ { 2 } - ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
E) $( x - 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } - ( z + 5 ) ^ { 2 } = 25$

Question

Find the standard form of the equation of the sphere with the given characteristics. 
Center: $( 4,3,5 )$ ;radius: 5

A) $( x - 4 ) ^ { 2 } - ( y + 3 ) ^ { 2 } - ( z - 5 ) ^ { 2 } = 25$
B) $( x - 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
C) $( x + 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
D) $( x - 4 ) ^ { 2 } - ( y - 3 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 25$
E) $( x - 4 ) ^ { 2 } + ( y - 3 ) ^ { 2 } - ( z + 5 ) ^ { 2 } = 25$

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 $(4, 3, 5)$ and radius $5$, the equation is $(x - 4)^2 + (y - 3)^2 + (z - 5)^2 = 25$.

Find the Standard Form of the Equation of the Sphere (4,3,5)( 4,3,5 )(4,3,5)

Find the Standard Form of the Equation of the Sphere $( 4,3,5 )$