# What is the vertex form of the equation of the parabola with a focus at (31,24) and a directrix of #y=23 #?

##### 1 Answer

May 28, 2017

#y=1/2(x^2-62x+1008)#

#### Explanation:

Look at the graph

The parabola is facing upwards, hence

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

Here

Vertex lies exactly at the middle of focus and directrix.

y coordinate of the vertex

Vertex

#(x-31)^2=4xx0.5xx(y-23.5)#

#x^2-62x+961=2y-47#

#2y-47=x^2-62x+961#

#2y=x^2-62x+961+47#

#y=1/2(x^2-62x+1008)#