Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.

Solution:

Given the focus of the parabola is (0, 3) and directrix y = -3

It is clear that the parabola is open upwards.

When focus is (0, a) and directrix is y = -a then the standard formula is

x² = 4ay

Here a = 3

Substituting the values

x² = 4(3)y

x² = 12y

So we get,

y = x²/12

Therefore, the equation of the parabola is y = x²/12.

Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.

Summary:

The equation for a parabola with its focus at (0, 3) and a directrix of y = -3 is y = x²/12.