Question

Find the set of points p such that the distance from p to a(-1,5,3) is twice the distance from p to b(6,2,-2)

Answer 1

A little playing around with plane figures (and/or distance equations) will convince you that this set of points is a sphere centered at

... c = (4b -a)/3 = (25/3, 1, -11/3) . . . . center

with a radius 2/3 of the length ab.

... r = (2/3)√(7² +3² +5²) = (2/3)√83 . . . . radius

Then the equation of this spherical set of points is

... (x -25/3)² +(y -1)² +(z +11/3)² = 332/9