what is the equation of the parabola with focus (0,0) , directrix x = 2 and horizontal has axis of symmetry

For a parabola with the x-axis as its axis of syemmetry (i.e. aligned horizontally), the general form is:


x-x_0 = \pm(\frac 1 {4p})(y-y_0)^2


where (x_0, y_0) is the focus and p is the distance between the focus and vertex, which also equals the distance from vertex to directrix. The positive version is for a paraboloa whose focus is to the right of the vertex, and the negative is for the case of the focus to the left of the vertex. So first determine the coordinates of the vertex (which is half way between directrix and focus), then you can use the above formula. Hope this helps.