# Axis horizontal, vertex (1, 2), latus rectum 6Find the Equation of the parabola

1
by gameongoplay
yes
Where does it open? There are 2 possible answers if you don't indicate where it opens.
Do you know where the focus of directrix is?
or*
it is the only given :(

2014-05-13T12:57:09+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
The equation of a parabola with vertex (h,k) with horizontal axis is

(y-k)² = 4p (x-h) , where |p| is the distance of the focus (or directrix) from the vertex.

1/2 Latus rectum = Distance from the directrix to the focus. (verify using the definition of parabola)

Since the vertex lies in the middle of the directrix and focus, |p| = 3.

Therefore the equation of the parabola is

(y-2)² = 4(±3) (x-1)
(y-2)² = ±12 (x-1)

Note: The sign indicates where the parabola opens. In this case, if it's +, then it opens to the right. Otherwise, it opens to the left.
Got it. Thanks much :))