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Topic: geometry help
Replies: 8   Last Post: Apr 26, 2014 11:56 AM

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 Peter Scales Posts: 192 From: Australia Registered: 4/3/05
Re: geometry help
Posted: Apr 26, 2014 11:56 AM

> > So the equation becomes either
> > C.Y^2 + D.X + E.Y + F = 0 with axis // oX, or
> > A.X^2 + D.X + E.Y + F = 0 with axis // oY
> >
> > In either case 4 points are necessary to determine
> > the equation...

>
> Without loss of genearlty we can divide out the above
> by F so that there remain three constants only.
>
> An inclined axis needs one more constant or one more
> point.
>

Narasimham,
Thanks for your comment. You are right that each of these equations has only 3 independent unknowns, but these equations are in the rotated coordinate system and are only to illustrate that, after rotation, we get a parabola with axis // to either oX or oY.

My first post addressed the situation with the parabola axis // oy, requiring only 3 points for determination.

To solve the general problem of how many points are necessary for a parabola of arbitrary orientation, we have the general 2nd degree equation, with 5 independent unknowns, and the equation setting the discriminant =0, leaving 4 independent unknowns to be determined, so we need 4 acceptable points, as you have said.

Regards, Peter Scales.

Date Subject Author
4/23/14 kelvin_m
4/23/14 Narasimham
4/24/14 Peter Scales
4/24/14 kelvin_m
4/24/14 kelvin_m
4/24/14 Narasimham
4/25/14 Peter Scales
4/26/14 Narasimham
4/26/14 Peter Scales