Conics in Polar Coordinates: Rotation, Example 5, and Eccentricity

In this video I go over further into Conics in Polar Coordinates but this combine a variety of topics together as part of my new video upload strategy. This video covers rotation of polar equations in general, rotation of conic sections in polar coordinates, and finally a brief illustration on how varying the eccentricity affects the shape (and type) of conic section being graphed. I am making this change because my deep dive into the wonderful world of #SuppressedScience and #SuppressedTechnology has been taking up much of my time. By lowering the number of videos but at the same time increasing the amount of content within each video, I am able to save time as well as move further and quicker along my calculus book. So expect some longer and more in-depth videos to come while I continue my epic ongoing research into #FreeEnergy and #AntiGravity!

Moving along, in this video I show that rotation of a polar equation is in fact very simple and we can just subtract an angle from the angle of any given function. This results in a rotation counterclockwise of the subtracted angle and about the origin (or polar pole). Either for polar equations in general, or specifically conic sections, this method applies throughout and is much easier to rotate conic sections in polar equations than in the more rigid Cartesian or rectangular coordinates.

Varying the eccentricity, or e, of a typical polar equation for a conic section yields some very interesting and surprising results. As e decreases below 1, the shape is an ellipse which is more elongated when e is closer to 1 but becomes more circular as e approaches zero. In fact as e approaches the zero the equation itself approaches zero so a circle is never reached but instead the graph appears to simply reach the exact point of the origin. When e = 1, the function is simply a parabola as expected. When e is greater than 1 the conic is a hyperbola that gets increasingly stretched out as e increases. INTERESTING STUFF!

This video is the first of my mathematics videos in this new format, so please let me know what you think by commenting below!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5x2M07Ol_vH_HG0Bg

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conics-in-polar-coordinates-rotation-example-5-and-eccentricity

Related Videos:

Conics in Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H4OJpJ2gslXVLT8mP-SgJP
Conic Sections Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FEUsuxP3KS5DRbidSSGBPL
Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUFiPLsYw5_Ljd5riOUzjP
Conics in Polar Coordinates: Example 2: Ellipse: https://youtu.be/iMy9HN30yIo
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY .

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