Question

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

Short answer

The required equation is:${(x-2)}^2+{(y-5)}^2+{(z+7)}^2=4$

Step-by-step solution

Given information

center (2, 5, −7) and tangent to the yz-plane

Finding the equation

The radius of sphere will be absolute value of x coordinate.

Radius = 2

The equation of sphere may be written as:

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

Simplify:

${(x-2)}^2+{(y-5)}^2+{(z+7)}^2=4$