Feynman's lost lecture The motion of the planets around the Sun

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To understand why ellipses have the light property we need to understand the concept of a tangent to a curve. Move point P round the ellipse. The red line is a tangent to the curve. It touches the curve at P. If we think of the ellipse as the path followed by a planet around the Sun, the tangent at each point will be the direction of the planet's instantaneous velocity at that point.

A ray from F hitting the ellipse at P will be mirror-reflected back to pass through F', just as if it was being reflected by the tangent line at P. The two marked angles will be equal.

Feynman wanted to prove that this reflecting property was equivalent to the string and tacks property.