Question

Describe the locus of points in R3 equidistant from the origin (0, 0, 0), and
the plane x + y + z = 1.

Answer 1

A parabola is the locus of points equidistant from a point and a line.

If you rotate it around its axis of symmetry, you get a surface with points equidistant from a point and a plane: a paraboloid.