I have 3 random points in an ellipse. Is it possible to find the radius of the ellipse?
How to find the radius(major and minor) with the given 3 points in an ellipse?
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conic-sections
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0No. Since there are two circles containing every three points not no a line, you can take any ellipse which isn't a circle and three points on it, then there will be a circle (i. e. another ellipse) through it having different radius. – 2012-05-02
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1If your ellipse is axis-aligned, you need **four** points to uniquely determine it; if not axis-aligned, you need **five** points. Your problem as it stands is underdetermined. – 2012-05-02
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1@martini: That's not right. Three points not on a line determine a unique circle. – 2012-05-02
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0@TonyK Upps ... you are right of course. – 2012-05-02
1 Answers
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The equation of an ellipse whose major and minor axes are parallel to the Cartesian axes is:
$$ \left(\frac{x-x_{0}}{a}\right)^{2}+\left(\frac{y-y_{0}}{b}\right)^{2}=1 $$
As you can see, the equation contains 4 different variables. Therefore, 3 points aren't sufficient to uniquely identify the ellipse.