Re: Determining an ellipse



A N Niel wrote: 
In article <425D5319.8050201@xxxxxxxxxxxxxxxxxxxxx>, Hop David
<hopspageHATESSPAaMmM@xxxxxxxxxxxxxxxxxxxxx> wrote:


Given:

A focus lies on the origin
The semimajor axis a
The eccentricity e
and two points on the ellipse's circumference.

With this info how is the ellipse's equation determined?

(I also posted this question in geometry.puzzles)

Thanks in advance,


Focus at the origin, eccentricity given. Try polar coordinates. 

OK.

r=p/(1+e*cos(f)) where p is semilatus rectum.

To rotate ellipse axis k radians from x axis I believe the equation becomes

r=p/(1+e*cos(f+k))?

and points on circumference (a1,a2) and (b1,b2)
become (sqrt(a1^2 + a2^2), atan(a1/a2)) and
(sqrt(b1^2 + b2^2), atan(b1/b2))?

Where to go from there isn't immediately obvious to me.

--
Hop David
http://clowder.net/hop/index.html

.

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