I need help regarding this doubt, i took a few examples and it holds true, but is it safe to conclude that two confocal parabolas cut each other orthogonally? Are there any conditions?
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Does this answer your question? https://en.wikipedia.org/wiki/Confocal_conic_sections#Confocal_parabolas – player3236 Feb 25 '21 at 12:00
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actually i went through this article but again i just want to confirm because i didn't fully understand that paragraph – Soumil Gupta Feb 25 '21 at 12:01
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Would two confocal parabolas that do not intersect be of interest to you? – Somos Feb 25 '21 at 12:17
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1For them to intersect orthogonally, they do have to share the same axis of symmetry, and face opposite directions. – Jaap Scherphuis Feb 25 '21 at 12:54
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Confocal conics are highly related to conformal mapping in complex analysis. Such as $z=w^2$ and $z=\cosh w$. – Ng Chung Tak Feb 25 '21 at 13:40
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See the optical proofs here. – Ng Chung Tak Feb 25 '21 at 13:50