Question

How do you find an equation of the sphere with center (1, −7, 4) and radius 5?

Answer 1

See a solution process below:

Explanation:

The general equation for a sphere of radius `color(red)(R)` with center at `(color(blue)(a), color(green)(b), color(purple)(c))` is:

`(x-color(blue)(a))^2 + (y-color(green)(b))^2 + (z-color(purple)(c))^2 = color(red)(R)^2`

Substituting the information from the problem gives:

`(x-color(blue)(1))^2 + (y-color(green)(-7))^2 + (z-color(purple)(4))^2 = color(red)(5)^2`

`(x-color(blue)(1))^2 + (y+color(green)(7))^2 + (z-color(purple)(4))^2 = color(red)(25)`