Question

Ind an equation of the sphere that passes through the point (6, 1, −1) and has center (5, 6, 5).

Answer 1

`(x - 5)^(2) + (y - 6)^(2) + (z - 5)^(2) = 62`

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) = 5, y_(c) = 6, z_(c) = 5`.

So

`(x - 5)^(2) + (y - 6)^(2) + (z - 5)^(2) = r^(2)`

through the point (6, 1, −1)

We use this to find the radius.

`(6 - 5)^(2) + (1 - 6)^(2) + (-1 - 5)^(2) = r^(2)`

`r^(2) = 1 + 25 + 36 = 62`

So the equation of the sphere is:

`(x - 5)^(2) + (y - 6)^(2) + (z - 5)^(2) = 62`