A parametric equation that describes a surface must have two parameters, call them and . Suppose you want a plane that runs through a point which contains two nonparallel lines and . (In the case of a square in the first quadrant of a Cartesian plane with a corner at the origin, your point will be anywhere in the square and the lines can be and .) Suppose the equations of the lines are given as and for constants and suppose the point's coordinates are . Then the parametric equations of the plane will be .
Probably the lesson here is that, whatever you're doing, you don't want to be doing it with parametric equations. I could be wrong.