Question

Find the equation of a sphere with center (2, 5, -7) and tangent to the xy-plane.

Short answer

The required equation is:

${(x-2)}^2+{(y-5)}^2+{(z+7)}^2=49$

Step-by-step solution

Given information

A sphere with center (2, 5, -7) and tangent to thexy-plane.

Finding the equation

The radius of sphere will be equal to the absolute value of the z coordinate $\left|-7\right|=7$.

The equation of sphere may be written as:

${(x-2)}^2+{(y-5)}^2+{(z+7)}^2=7^2$

Simplify:

${(x-2)}^2+{(y-5)}^2+{(z+7)}^2=49$