Since the directrix is vertical, use the equation of a parabola that opens up or down.

The vertex is halfway between the directrix and focus. Find the coordinate of the vertex using the formula . The coordinate will be the same as the coordinate of the focus.

Simplify the vertex.

Subtract from .

Move the negative in front of the fraction.

The distance from the focus to the vertex and from the vertex to the directrix is . Subtract the coordinate of the vertex from the coordinate of the focus to find .

Simplify.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Move the negative in front of the fraction.

Substitute in the known values for the variables into the equation .

Simplify.

Find the Parabola with Focus (3,-7) and Directrix y=-4 (3,-7) y=-4