Question

Find an equation of the sphere through the point (4,3,-1) and has center (3,8,1).

Answer 1

`(x - 3)^(2) + (y - 8)^(2) + (z - 1)^(2) = 30`

Explanation:

The general equation of a sphere is as follows:

`(x - x_(c))^(2) + (y - y_(c))^(2) + (z - z_(c))^(2) = r^(2)`

In which the center is
`(x_(c), y_(c), z_(c)`, and r is the radius.

In this problem, we have that:

`x_(c) = 3, y_(c) = 8, z_(c) = 1`

So

`(x - 3)^(2) + (y - 8)^(2) + (z - 1)^(2) = r^(2)`

through the point (4,3,-1)

This leads us to find the radius.

`(4 - 3)^(2) + (3 - 8)^(2) + (-1 - 1)^(2) = r^(2)`

`r^(2) = 1 + 25 + 4`

`r^(2) = 30`

So the equation of the sphere is:

`(x - 3)^(2) + (y - 8)^(2) + (z - 1)^(2) = 30`