Question

Find the equation of a sphere containing the point (1, 4, 7) and whose center is (-2, 3, 5).

Short answer

The required equation is:${(x+2)}^2+{(y-3)}^2+{(z-5)}^2=14$

Step-by-step solution

Given information

A sphere containing the point (1, 4, 7) and whose center is (-2, 3, 5).

Finding the radius

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

Radius is:

$\sqrt{{(1+2)}^2+{(4-3)}^2+{(7-5)}^2}$

Simplify:

$\sqrt{14}$

Finding the equation

The equation of the sphere may be written as:

${(x+2)}^2+{(y-3)}^2+{(z-5)}^2={\left(\sqrt{14}\right)}^2$

Simplify:

${(x+2)}^2+{(y-3)}^2+{(z-5)}^2=14$