,

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.

Cancel the common factor of and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Add and .

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 .

Subtract from .

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

Simplify.

Find the Parabola with Focus (2,4) and Directrix y=8 (2,4) , y=8