Question

Equation of a Sphere Find an equation of a sphere with the given radius r and center C.

$r=3;C(-1,4,-7)$.

Short answer

The equation of the square with center $C(-1,4,-7)$ and radius $r=3$ is

${(x+1)}^2+{(y-4)}^2+{(z+7)}^2=9.$

Step-by-step solution

Step 1. Given information.

The center $C(-1,4,-7)$ and the radius 3 are given.

Step 2. We have to find the equation of the sphere.

Substitute the center and the radius in the equation of the sphere formula.

Given,
Center= $C(-1,4,-7)$
Radius $r=3$
The equation of the sphere is given by,

${(x-h)}^2+{(y-k)}^2+{(z-l)}^2=r^2$

Substitute the center $C(-1,4,-7)$and radius $r=3$in the equation, we get

${(x-(-1\left)\right)}^2+{(y-4)}^2+{(z-(-7\left)\right)}^2=3^2$

${(x+1)}^2+{(y-4)}^2+{(z+7)}^2=9$