Question

Find an equation of the sphere which contains points A(1, 3, 2) and B(4, 3, 7) and the distance between A and B is equal to the diameter of the sphere

Answer 1

The answer is 8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2

Explanation:

First we need to find diameter of the sphere. The distance point A and point B is:

`d=√((4-1)^2+(3-3)^2+(7-2)^2) \\d=√(3^2+0^2+5^2) \\d=√(34) \\d=5.83`

d/2=r=2.92

radius of the sphere is 2.92 units

and the center of the sphere is:

C=((4+1)/2,(3+3)/2,(7+2)/2)

C=(2.5,3,4.5)

We can write the equation of the sphere as:

`r^2=(x-2.5)^2+(y-3)^2+(z-4.5)^2\\8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2`