Question

Find an equation of the sphere that passes through the point (7, 1, −3) and has center (5, 6, 5).

Answer 1

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is
`(x-5)^(2)+(y-6)^(2)+(z-5)^(2) = 93`.

Explanation:

Any sphere centered at
`(h,k,s)` in an Euclidean space with a radius
`r` is represented by the following formula:

`(x-h)^(2) +(y-k)^(2)+(z-s)^(2) =r^(2)`

If
`(x,y,z) = (7,1,-3)` and
`(h,k, s) = (5,6,5)`, the radius of the sphere is obtained:

`(7-5)^(2)+(1-6)^(2)+(-3-5)^(2) = r^(2)`

`r^(2) = 93`

`r = √(93)`

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is
`(x-5)^(2)+(y-6)^(2)+(z-5)^(2) = 93`.