Suriin ang malawak na saklaw ng mga paksa at makakuha ng mga sagot sa IDNStudy.com. Ang aming mga eksperto ay handang magbigay ng malalim na sagot at praktikal na solusyon sa lahat ng iyong mga tanong.

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


Sagot :

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.