An ellipse with its focal points and a tangent line. What is the angle α?
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Solution
The angle α is 90°.
We draw four lines perpendicular to the tangent as shown. Now because the tangent acts like a mirror for rays coming from the focal points, one can extend the line AB to C. It is obvious that |F’C|=2c=2|AF’|, implying that b-x=x. So the perpendicular line through F’ indeed cuts the semi-minor axes halfway.
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