A Rectangle in an Ellipse?

★ 7/10Parametrization conic sections analytic geometry Discriminant

Problem

Let $A, B, C$ be three points on the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ ( $a > b > 0$ ), and let $O$ be the origin. Can the quadrilateral $OABC$ be a rectangle? Justify your answer.

Answer

Solution

Difficulty	7/10
Topics	Parametrization, conic sections, analytic geometry, Discriminant

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