Question

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

$r=\sqrt{11};C(-10,0,1)$.

Short answer

The equation of the square with centre $C(-10,0,1)$and radius $r=\sqrt{11}$is

${(x+10)}^2+y^2+{(z-1)}^2=11$

Step-by-step solution

Step 1. Given information.

The centre $C(-10,0,1)$ and the radius $r=\sqrt{11}$ are given.

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

Substitute the centre $C(-10,0,1)$and the radius $r=\sqrt{11}$in the equation of the sphere formula.

Given,
Centre =$C(-10,0,1)$
Radius$r=\sqrt{11}$
The equation of the sphere is given by,

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

Substitute the centre $C(-10,0,1)$and radius $r=\sqrt{11}$in the equation, we get

${(x-(-10\left)\right)}^2+{(y-0)}^2+{(z-1)}^2={\left(\sqrt{11}\right)}^2$

${(x+10)}^2+y^2+{(z-1)}^2=11$