# 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

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

for some

This will have its focus at

We are given that the focus is at

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

Subtract

#1/(4a) = 3#

Multiply both sides by

#1/4 = 3a#

Divide both sides by

#1/12 = a#

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

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