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 zāaxis respectively, then P is the orthocenter of the triangle XYZ. Putnamgeometry3D geometrytangent