# What is the equation in standard form of the parabola with a focus at (14,-19) and a directrix of y= -4?

##### 1 Answer

Jul 7, 2018

#(x-14)^2=30(y+11.5)#

#### Explanation:

Given -

Focus

Directrix

Find the equation of the parabola.

Look at the graph.

From the given information, we can understand the parabola is facing downward.

The vertex is equidistance from directrix and focus.

Total distance between the two is 15 units.

Half of 15 units is 7.5 units.

This is

By moving down 7.5 units down from

Hence vertex is

The vertex is not at the origin. Then, the formula is

#(x-h)^2=4a(y-k)#

Plug in the values.

#(x-14)^2=4(7.5)(y+11.5)#

#(x-14)^2=30(y+11.5)#