The distance of any point on the parabola from its focus and its directrix is same.
Given that, directrix, x = 0 and focus = (6, 0)
If a parabola has a vertical axis, the standard form of the equation of the parabola is (x - h)2 = 4p(y - k), where p≠ 0.
The vertex of this parabola is at (h, k).
The focus is at (h, k + p) & the directrix is the line y = k - p.
As the focus lies on x – axis,
Equation is y2 = 4ax or y2 = -4ax
So, for any point P(x, y) on the parabola
Distance of point from directrix = Distance of point from focus
x2 = (x – 6)2 + y2
x2 = x2 - 12x + 36 + y2
y2 - 12x + 36 = 0
Hence the required equation is y2 - 12x + 36 = 0.