MathDB

Determine the equations of a surface in three-dimensional cartesian space which has the following properties: (a) it passes through the point

(1,1,1)

and (b) if the tangent plane is drawn at any point

P

and

X,Y, Z

are the intersections of this plane with the

x, y

and

z-

axis respectively, then

P

is the orthocenter of the triangle

XYZ.

Problem Statement