# What is the equation of the parabola with a focus at (5,3) and a directrix of y= -12?

##### 1 Answer

#### Explanation:

The definition of a parabola states that all points on the parabola always have the same distance to the focus and the directrix.

We can let

We can now setup an equation with these points. We will use the distance formula to work out the distances:

We can apply this to our points to first get the distance between

Then we'll work out the distance between

Since these distances must be equal to each other, we can put them in an equation:

Since the point

First, we'll square both sides:

We can then expand:

If we put everything on the left and collect like terms, we get:

which is the equation of our parabola.