Aparabola has a focus of f(2, -0.5) and a directrix of y=-1.5 p(x, y) represents any point on the parabola, while d(x, -1.5) represents any point on the directrix.

what are the steps required to find the equation of the parabola?

The sketch of the parabola is attached below

We have the focus 
The point 
The directrix, c at 

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;  and .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by


Step 2
Find the distance between the point P to the directrix . It is a vertical distance between y and c, expressed as 

Step 3
The equation of parabola is then given as 
=
 ⇒ substituting a, b and c

⇒Rearranging and making  the subject gives