Find an equation for the sphere with the given center and radius.
-Center (0, -8, -1), radius = 10
A) $x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y + 2 z = 35$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 16 y + 2 z = 35$
C) $x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y - 2 z = 35$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 16 y - 2 z = 35$

Question

Find an equation for the sphere with the given center and radius.
-Center (0, -8, -1), radius = 10 
A) $x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y + 2 z = 35$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 16 y + 2 z = 35$
C) $x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y - 2 z = 35$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 16 y - 2 z = 35$

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 the given center $(0, -8, -1)$ and radius $10$, we get $(x - 0)^2 + (y + 8)^2 + (z + 1)^2 = 10^2$, which simplifies to $x^2 + y^2 + z^2 + 16y + 2z + 64 + 1 = 100$, or $x^2 + y^2 + z^2 + 16y + 2z = 35$, matching option B.

Find an Equation for the Sphere with the Given Center x2+y2+10z2+16y+2z=35x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y + 2 z = 35x2+y2+10z2+16y+2z=35

Find an Equation for the Sphere with the Given Center $x ^ { 2 } + y ^ { 2 } + 10 z ^ { 2 } + 16 y + 2 z = 35$