Question

What is the equation of the parabola with vertex (2, 4) and focus (5, 4)?

Answer 1

Ans is (y-4)2=12(x-2).
Translate the cartesian plane by converting (2,4) to (0,0). focus will change to (3,0).
So in translated plane it will be standard right handed parabola with equation y2=4ax. So in trnaslated plane its equation comes y2=12x. Again substitute and get the answer.

Answer 2

is it x=1/6y^2? correct?

Answer 3

(y-4)2 = 12 (x-12)