Find an equation for the sphere with the given center and radius.
-Center (0, 0, 10), radius = 8
A) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 20 z = - 36$
B) $x ^ { 2 } + y ^ { 2 } + 8 z ^ { 2 } - 20 z = - 36$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 20 z = - 36$
D) $x ^ { 2 } + y ^ { 2 } + 8 z ^ { 2 } + 20 z = - 36$

Question

Find an equation for the sphere with the given center and radius.
-Center (0, 0, 10), radius = 8 
A) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 20 z = - 36$
B) $x ^ { 2 } + y ^ { 2 } + 8 z ^ { 2 } - 20 z = - 36$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 20 z = - 36$
D) $x ^ { 2 } + y ^ { 2 } + 8 z ^ { 2 } + 20 z = - 36$

Quizplus · Accepted Answer

The equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. Substituting $h = 0$, $k = 0$, $l = 10$, and $r = 8$ gives $(x - 0)^2 + (y - 0)^2 + (z - 10)^2 = 8^2$, which simplifies to $x^2 + y^2 + z^2 - 20z = -36$.

Find an Equation for the Sphere with the Given Center x2+y2+z2−20z=−36x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 20 z = - 36x2+y2+z2−20z=−36

Find an Equation for the Sphere with the Given Center $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 20 z = - 36$