Question

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

Answer 1

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`