find an equation for a shifted conic

Question

directrix=-12 and vertex at (-6,0)

Answer 1

it's a parabola horizontal opening rightward

general formula is x = ay^2 -6

with directrix x =-12, the focus is (0, 0) and another point on the parabola is (0, 12)

plug that in to find "a"

0 = 144a -6

a = 6/144 = 3/72 = 1/24

x = (y^2)/24 - 6