Question

Find an equation of a sphere if one of its diameter has endpoints (2,1,4) and (4,3,10)

Answer 1

`(x-3)^2+(y-2)^2+(z-7)^2 =11`

Explanation:

Given that a sphere has one diameter having endpoints (2,1,4) and (4,3,10)

We can find the mid point of these two points and that would be the centre

If we find distance between these two points that would be twice radius.

Distance = 2r =
`√((4-2)^2+(3-1)^2+(10-4)^2) \\=√(44)`

So radius =
`√(11)`

Centre of sphere = mid point of two points

= (3, 2, 7)

Using centre radius formula sphere has equation as

`(x-3)^2+(y-2)^2+(z-7)^2 =11`