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Ellipse Billiards
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On a 3D elliptical billiard table, draw the cushion with two pins and a string to find what an ellipse is (PF + PF′ = 2a) and c² = a² − b², then find the tangent line at a point on the cushion from the discriminant D = 0. Shoot and send light to discover that a ball shot from one focus always passes through the other focus and that a parabolic dish gathers light parallel to its axis at the focus.
Key conceptsellipse · foci of an ellipse · major and minor axes · equation of an ellipse · equation of a tangent line · discriminant · parabola · directrix