Parabola? x^2=4ay (1 Viewer)

[rsingh]

Hey guys,

You know the parabola x^2=4ay .. could someone explain why we put the parabola in this form, and all of its features, like focus, directrix, focal length, latus rectum?

I just don't get it. It's weird.

Thanks.

 

[Xayma]

The parabola x²=±4ay, or the general from (x-j)²=4a(y-k) is put in that form because it becomes easier to recognise the features.

For the parabola (x-j)²=4a(y-k), [x²=4ay being where j=k=0]

Its vertex lies at (j,k)
It has a focal length of a units and a focus at (j,k+a), the focus is the point at which any lines coming into the parabola parallel to the y-axis will be reflected into.
The directix (the directix and the focus being equal length away from any point on the parabola) is at y=k-a.

Latus Rectum is the focal chord (a chored passing through the focus) that is parallel to the directix.

 

[rsingh]

Thanks a lot.

So we use this form because it's easier to recgonise the features than ax^2+bx+c=0?

But they're both the same?

 

[Trev]

yea its both the same, but if u need to draw it or work out applications in relation to the parabola its easier ps. the x2=±4ay or (x-j)2=4a(y-k) form both have 'y' in it, the form u just mentioned doesnt - so u cant write parabolas in that form then (correct me if im wrong)

 

[mojako]

form both have 'y' in it, the form u just mentioned doesnt

it should have y.
it should be y=ax^2+bx+c,
NOT ax^2+bx+c=0
since ax^2+bx+c=0 is NOT a parabola AT ALL
(well... one can say that it's a kind of parabola.. it's a matter of interpretation)

EDIT:
whoops.. I didn't read this line:

so u cant write parabolas in that form then

sorry

 

[withoutaface]

I think you can write parabolas in that form, it just moves the parabola up the axes, or to the side. I think the definition of a parabola is the graph of a quadratic equation.