Show that the points (3,2,2), (-1,4,2), (0,5,6), (2,1,2) lie on a sphere whose centre is (1,3,4). Find the also its radius.

Explanation

Let the points be `A(3,2,2), B(−1,4,2), C(0,5,6) and D(2,1,2)` lie on the sphere,
whose centre be `P(1,3,4)`.

Since, `AP,BP,CP and DP` square measure radii

Hence, `AP=BP=CP=DP`
Now, `AP=sqrt((3-1)^2+(2-3)^2+(2-4)^2`
`=sqrt(4+1+4)`
`=sqrt(9)`
`=3`
`BP=sqrt((-1-1)^2+(4-3)^2+(2-4)^2`
`=sqrt(4+1+4)`
`=sqrt(9)`
`=3`
`CP=sqrt((0-1)^2+(5-3)^2+6-4)^2`
`=sqrt(4+1+4)`
`=sqrt(9)`
`=3`
`DP=sqrt((2-1)^2+(1-3)^2+(2-4)^2`
`=sqrt(4+1+4)`
`=sqrt(9)`
`=3`
Here, we will clearly see that
`AP=BP=CP=DP`

Hence, `A(3,2,2), B(−1,4,2), C(0,5,6) and D(2,1,2)` lie on the sphere whose radius is `3` units.