Question

Find the equation of a sphere containing the point (3, 0, -1) and whose center is (2, -8, 0).

Short answer

The required equation is:${(x-2)}^2+{(y+8)}^2+z^2=66$

Step-by-step solution

Given information

A sphere containing the point (3, 0, -1) and whose center is (2, -8, 0).

Finding the radius

The radius will be the distance between the given point and center.

Radius is:

$\sqrt{{(3-2)}^2+{(-8-0)}^2+(0-{(-1))}^2}=\sqrt{66}$

Finding the equation

The equation of sphere may be written as:

${(x-2)}^2+{(y+8)}^2+{(z-0)}^2={\left(\sqrt{66}\right)}^2$

Simplify:

${(x-2)}^2+{(y+8)}^2+z^2=66$