What is the equation of a parabola with a vertex at (3,4) and a focus at (6,4)?

1 Answer
Nov 29, 2015

In vertex form:

#x = 1/12 (y-4)^2+3#

Explanation:

Since the vertex and focus lie on the same horizontal line #y = 4#, and the vertex is at #(3, 4)# this parabola can be written in vertex form as:

#x = a(y-4)^2+3#

for some #a#.

This will have its focus at #(3+1/(4a), 4)#

We are given that the focus is at #(6, 4)#, so:

#3+1/(4a) = 6#.

Subtract #3# from both sides to get:

#1/(4a) = 3#

Multiply both sides by #a# to get:

#1/4 = 3a#

Divide both sides by #3# to get:

#1/12 = a#

So the equation of the parabola may be written in vertex form as:

#x = 1/12 (y-4)^2+3#