Let and be the endpoints of a diameter of a sphere that passes through the point

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

Let

A(2t,3,-1)

and

B(4,-1,t)

be the endpoints of a diameter of a sphere that passes through the point

P(3,1,1)

, where

t

is a real parameter. (i) Determine the value(s) of

t

for which

P

lies on the sphere. (ii) For each admissible value of

t

, write the corresponding equation of the sphere.