(723, #43) Find an equation for the surface consisting of all points that are equidistant from the point
( -1, 0, 0 ) and the plane x = 1. Identify the surface.

Solution: Find the distance from the point (x,y,z) to the point (-1,0,0).

distance =

Next, the distance from the point (x,y,z) to the plane x = 1 is the

length of the line from (x,y,z) to (1,y,z) so

distance =

=

The equation of the surface is . Thus the surface is a paraboloid.

Maple code

by: gm