From a geometric standpoint,is there only one "true" parabola like there is only one "true" circle? In the sense,all circles are similar to each other by suitable dilations and translations.How can we infer the same for parabola?
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1Relevant video on this very topic by standupmaths on YouTube -- https://www.youtube.com/watch?v=hoh4TmPzu1w – PrincessEev Mar 12 '19 at 05:29
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1More generally, there is only one conic up to similarity with a given eccentricity $e$ ($e=1$ for parabola, $e=0$ for circle). – Angina Seng Mar 12 '19 at 05:31
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Ah, I get it now.Translate the focus and directrix of the parabola and we are done!Thanks for all the help guys. – Venkaat Balaje Mar 12 '19 at 05:33
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https://en.m.wikipedia.org/wiki/Parabola#Similarity_to_the_unit_parabola – amd Mar 12 '19 at 06:26