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for my Math 2U assignment, we have to discuss real life applications of different conic sections.

However, apart from the wheel, I cannot find or think of any other real life applications of the circle.

Does anybody have any suggestions?

Cheers

FYI: The question is: Explain two applications of each conic section.

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    $\begingroup$ Clock, $\pi$, I mean pie,... $\endgroup$ – copper.hat Jun 18 at 23:24
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    $\begingroup$ Basketball hoop. $\endgroup$ – Michael Jun 18 at 23:26
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    $\begingroup$ manhole cover is round for a mathematical reason.... $\endgroup$ – achille hui Jun 18 at 23:26
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    $\begingroup$ I think we have covered them all now. $\endgroup$ – Michael Jun 18 at 23:27
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    $\begingroup$ Shortest distance between two points on a sphere is part of a great circle. $\endgroup$ – copper.hat Jun 18 at 23:58
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It depends a bit on how "practical" you want the application to be, considering that conics are a theoretical concept in a 2D space.

Strictly regarding applications of conics, here are a few thoughts:

  • the planetary orbits are elliptical. Have a look at Kepler's laws for planetary motion, which have some interesting results.
  • the projectile motion (ballistic curve, e.g. cannon ball) is a parabola.
  • if there is an object (e.g. a comet) flying with high velocity through space near another, bigger object (e.g. star), the attraction of the bigger object would lead to a hyperbolic trajectory for the smaller object. If the smaller object travels slow enough, it is captured in an elliptical orbit. This is easy to explain with celestial bodies, but happens with electric charges too.
  • parabolas have an interesting property: imagine you build a parabola shaped mirror. Simply following the light reflection laws, all rays reflected by the parabolic mirror go though the focal point. And that's why we have parabolic antennas
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