Find the equation of the parabola with focus F(0, -3) and directrix y = 3.

Question

Philoid · Accepted Answer

Given equation of directrix : y = 3

• y - 3 = 0

Above equation is of the form, y - a = 0

Focus of the parabola F(0,-3) is of the form F(0,-a)

Therefore, a = 3

For directrix with equation y-a=0 and focus (0,-a), equation of the parabola is,

x² = - 4ay

• x² = - 12y