What is the equation of the parabola which has the origin at directrix and focal chord at X axis?

This doesn't make much sense - please clarify the question. Teh focal point of a parabola is a point, not a chord' and the directrix is a chord, not a point. So perhaps you have these terms vbackwards. But even so - if the focal point lies on the directrix as you have indicated the resulting parabola is not a parabola at all but rather merely a line.