BMAD 62 Report post Posted September 11 How many points would you need to have to uniquely determine an ellipse given that you know a foci is located at (0,0). Share this post Link to post Share on other sites

0 gavinksong 11 Report post Posted September 13 (edited) Minor grammar correction: the singular form of foci is focus. Without really thinking about it, I'm going to guess: Spoiler Two points. The intuition is that one point would contain less information than the minimal definition of an ellipse (minus a focus), whereas two points contains more. Edited September 13 by gavinksong wording Share this post Link to post Share on other sites

0 gavinksong 11 Report post Posted September 13 After some more thought, Spoiler Three points. With each point, we get the equation: R = |p| + |p - f| where R and f are unknown values, and p is the new point in vector form. There are three unknowns (since f is 2-dimensional), which we need at least three equations to solve. Share this post Link to post Share on other sites

0 bonanova 76 Report post Posted September 13 Spoiler Ellipse is the locus of points the sum of whose distances from the foci is constant. So, we just need (a) the other locus and (b) any point on the ellipse to determine the sum: two more points. Share this post Link to post Share on other sites

0 Quantum.Mechanic 0 Report post Posted September 15 Spoiler It's odd that given one focus, and two points on the ellipse, is not enough. But three points on the ellipse, with one focus, should be enough to determine the ellipse and the other focus. And four points on the ellipse, and no foci, would also work. But how to do this is beyond me. Share this post Link to post Share on other sites

0 gavinksong 11 Report post Posted September 17 (edited) On 9/16/2017 at 12:56 AM, Quantum.Mechanic said: Hide contents It's odd that given one focus, and two points on the ellipse, is not enough. But three points on the ellipse, with one focus, should be enough to determine the ellipse and the other focus. And four points on the ellipse, and no foci, would also work. But how to do this is beyond me. My thoughts exactly... except is it possible with four points? Edited September 17 by gavinksong Share this post Link to post Share on other sites

How many points would you need to have to uniquely determine an ellipse given that you know a foci is located at (0,0).

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