find cartesian equation of a hypeerbola with centre as origin , focus : ( 2, 0 ) and line x = 2 as directrix .
I think you have a mistake. An hyperbola has two directrices, and they are always slanted if the focus is on an axis. You must mean a parabola.
Nope, that is also bogus. A parabola has no center, and the focus cannot lie on the directrix.
Better clean up your problem.