The endpoints of a diameter of a sphere are and

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

Problem

The endpoints of a diameter of a sphere are

A(2,-1,4)

and

B(x,3,6)

. The centre of the sphere lies on the plane

x+2y-z=3

. (i) Determine the value of

x

. (ii) Hence, write the equation of the sphere.