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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
3 years, 5 months ago