Question

What is the equation of the quadratic graph with a focus of (2, 0) and a directrix of y = −12?

Answer 1

Distance from  the point (x,y) to the focus  = distance of (x,y) from the directrix
so we have

sqrt  [(x - 2)^2 + y2]  = 12 + y

squaring both sides
x^2 - 4x + 4 + y^2 = 144 + 24y + y^2

x^2 - 4x + 4 = 144 + 24y

24y = x^2 -4x - 140

y = x^2/24 - x/6 -  35/6    is the required equation