Question

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

$r=5;C(2,-5,3)$.

Short answer

The equation of the square with center $C(2,-5,3)$ and radius $r=5$ is

${(x-2)}^2+{(y+5)}^2+{(z-3)}^2=25$

Step-by-step solution

Step 1. Given information.

The center $C(2,-5,3)$ and the radius 5 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= $C(2,-5,3)$
Radius $r=5$
The equation of the sphere is given by,

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

Substitute the center $C(2,-5,3)$and radius $r=5$ in the equation, we get

$\begin{array}{l}{(x-2)}^2+{(y-(-5\left)\right)}^2+{(z-3)}^2=5^2\\ {(x-2)}^2+{(y+5)}^2+{(z-3)}^2=25\end{array}$