Since the line passing through the focus and perpendicular to the directrix is x-axis,

therefore axis of the required parabola is x-axis.

Let the coordinate of the focus is S(a, 0).

Since the vertex is the mid point of the line joining the focus and the point (2, 0) where the directix is x - 2 = 0 meets the axis.

So, 0 = {a - (-2)}/2

=> 0 = (a + 2)/2

=> a + 2 = 0

=> a = -2

Thus the coordinate of focus is (-2, 0)

Let P(x, y) be a point on the parabola.

Then by definition of parabola

     (x + 2)² + (y - 0)² = (x - 2)²

=> x² + 4 + 4x + y² = x² + 4 - 4x

=> 4x + y² = - 4x

=> y² = -4x - 4x

=> y² = -8x

This is the required equation of the parabola.