MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry
Problem
Consider the inequality (x−3)2+(y+4)2+(z−2)2<64.
(i) Identify the centre and radius of the sphere determined by the given inequality.
(ii) Determine whether the points A(6,0,2) and B(3,0,10) satisfy the inequality. Show your working.
(iii) Find the equation of the smallest sphere centred at the origin that completely contains all points satisfying the given inequality.