# What is the equation in standard form of the parabola with a focus at (18,24) and a directrix of y= 27?

##### 1 Answer

#### Explanation:

We know that the standard form for the equation of a parabola with a horizontal directrix is

but, because we are given the focus and the equation of the directrix, it is easier to start with the corresponding vertex form

and then convert to standard form.

We know that the x coordinate, "h", of the vertex is the same as the x coordinate of the focus:

Substitute into equation [1]:

We know that the y coordinate, "k", of the vertex is the midpoint between the focus and the directrix:

Substitute into equation [2]:

The focal distance, "f", is the signed vertical distance from the vertex to the focus:

We know that

Substitute into equation [3]:

Expand the square:

Distribute the

Combine like terms: