Find the equation of the sphere passing through P4 3 2 and Q

Find the equation of the sphere passing through P(4, 3, 2) and Q(6, 5, 1) with its center at the midpoint of PQ.

Solution

Solution:

The mid point of PQ = (-4+6 /2 , 3-5 /2 , 2+1 /2)

=> (x1,y1,z1) = (1,-1,3/2)

Hence the equation of the sphere would be simply:

(x-x1)² + (y-y1)² + (z-z1)² = r²

Here;

r = Distance between Q and center = Distance between and center

=> (x-1)² + (y+1)² + (z-3/2)² = (5²+6²+0.5²)

=> (x-1)² + (y+1)² + (z-3/2)² = 61.25