Question

Find the locus of a point, the sum of distances from (1, 0, 0) and (–1, 0, 0) is 10.

Answer 1

Let the point be P(x, y, z).

Consider A = (1, 0, 0) and B = (–1, 0, 0) 

Given 

PA + PB = 10

which is the locus of the given point.