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Arbitrary focals?

Let \(\alpha\) denote the absolute value of the difference between the lengths of the segments of a focal chord of a parabola. Let \(\beta\) denote the length of a chord passing through the vertex and parallel to that focal chord. Then which of the following is always true?

  • \(\alpha^2 = 2 \beta\)

  • \(\alpha = 2 \beta\)

  • \(\alpha = \beta\)

  • \(\beta^2 = 2 \alpha\).

Note by Paramjit Singh
2 years, 11 months ago

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