Find the equation of the parabola having the directrix and vertex given by (x-2=0); V (2,-2) and what are the coordinates of the focus?

The basic equation for the parabola is:



Where (x1, y1) are the coordinates of the vertex (which you have been given) and p is the distance from the focus to the vertex, which is also equal to the distance from the vertex to the directrix. From the data you've provided it seems that the vertex at (2, -2) lies on the directrix line (x = 2). So you don't have a parabola at all! Please recheck the data - I wonder if instead of x-2 =0 you should have written y-2 =0?