It should read L₂/L₁. For y=x² the focal length is 1/4 so L₁=1/2 and the arc length from x=-1/2 to x=1/2 is L₂=(ln(1+√2)+√2)/2. Its universal, because all parabolas can be obtained from y=x² by shifting or scaling as explained by @standupmaths here: https://youtu.be/hoh4TmPzu1w .
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Expected distance from a randomly selected point in the unit square to its center (square point picking) is P/6 (where P is Universal Parabolic Constant = √2 + ln (1 + √2) Lindemann-Weierstrass Theorem shows that Universal Parabolic Constant is Transcendental Number.
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l1 is twice the focal length, say 2P. The latus rectum is always 4P (the blue line). l2 is to be longer than the blue line, thus larger than l1. Your fraction has to be less than 1 or you have it the other way around.
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Seems like the ratio is backwards in the image; l_1 and l_2 should be inverted, no?
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Do you think this is a sign?
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The problem however is: How to find d multiple of 2.2955....
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Oh wow that is just so unknown
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Great pic illustrating ratio variables clearly (Parabolic chord : 2a). My quick look up: http://mathworld.wolfram.com/LatusRectum.html …
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