How do I get all points in an ellipse knowing one point and the two focal.

Question

I have to develop an algorithm that return all the points of a ellipse knowing one point and the two focal points.
That's what I already have to work with:

$P(x, y)$

$F_1(x',y')$

$F_2(x'',y'')$

Is it possibly? If so, how to do it?

Sorry if I miss something, I'm not really much of a mathematician.

Answer 1

The ellipse in question consists of all the points such that the sum of the distances from the foci is constant. You know the foci, and can easily compute the constant from the known point on the ellipse.

Then you have an equation in the coordinates $(x,y)$ of the general point on the ellipse.

Whether that counts as an algorithm "returning all the points" depends on the use you want to make of the information. You can use it to generate points, or to test if a point is on the ellipse.

Answer 2

No. It's impossible.

Algorithm, by definition, must perform finite number of steps, so it can produce only finite set of output data. And an ellipse contains infintely (even worse: uncountably infinitely!) many points.

Hence no algorithm can find all points of an ellipse.