(a) Define the term "locus of a point" in three–dimensional…

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

Problem

(a) Define the term "locus of a point" in three–dimensional space. (a) Define the term "locus of a point" in three–dimensional space. (b) Let

A(h, k, l)

be a fixed point and let

r>0

be a given real number. Derive, step by step, the Cartesian equation of the set of all points

P(x, y, z)

such that

PA=r

. (c) Write the equation obtained in part (b) when

A

coincides with the origin and briefly interpret the result.