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Conic Sections: Parabolas: Example 2: Paraboloid Headlights and Telescopes (Problems Plus)

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First published at 00:37 UTC on November 24th, 2017.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over another example on parabolas, and this time go over a very useful application of parabolas, which is the property that lines extending from the focus of a parabola to a point on the parabola get protruded in a horizontal line. This property makes it very useful to design headlights and telescopes in a paraboloid shape; which is a 3D parabola formed by rotating a parabola about its central axis. In this particular video I prove that this is the case by proving the angle between a line tangent to point on the parabola and a line extending to that point from the focus is equivalent to the angle between the tangent line and a horizontal line protruding from that point on the parabola. Many cars and large-scale mirror telescopes use this design property of the parabola, and thus it is pretty cool to see the math behind just why it works! This is a very interesting video in it is a more advanced example, part of the Problems Plus section of my Calculus book, as well as its real world applications so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvh4UkkM5vzwV2H3Yw

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-conic-sections-parabolas-example-2-paraboloid-headlights-and-telescopes-problems-plus