I am not sure if you just want to write the equation, or if you actually want to develop the equation.
I will assume the latter.
if focus is (5,0) and vertex is (0,0), the the directrix is x = -5
Let P(x,y) be any point on the parabola
x+5 = √( (x-5)^2 + y^2)
square both sides
x^2 + 10x + 25 = x^2 - 10x + 25 + y^2
20x = y^2 is your equation
What is the equation for the parabola with vertex (0, 0) and focus (5, 0)
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