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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!
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Related Videos:
Conic Sections: Parabolas: Example 1: y2 + 10x = 0: https://youtu.be/JnSB2aVzxoE
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Angle Between Two Lines: Formula in terms of Slopes: https://youtu.be/O8M4ZErxE-M .
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