Question

Find the equation of a parabola with vertex at the origin and the directrix, y = 2.

Answer 1

Let the equation of the directrix be y = a.

Comparing with y = 2:
a = 2

Equation of the parabola with directrix y =a is $x^2=-4ay$.

Hence, the required equation of the parabola is $x^2=-8y$.