Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2

Solution:

Given that, Focus = (0, -2) lies on y-axes.

∴ Required equation of the parabola is of the form x² = 4ay

Now focus of such parabola = (0, a) = (0, -2)

∴ a = -2

Required equation is x² = 4(-2)y

x² = -8y

Aliter

Directrix of given parabola is y = -a

Here y = 2 = -a ⇒ a = -2

∴ Required equation is x² = 4(-2)y

x² = -8y

Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2

Summary:

The standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2 is x²= -8y.