In this video I go over further into Conic Sections in Polar Coordinates and this time expand in detail on the variations in the polar equations theorem that stems from the unified theorem for conics which I covered in my last video. Recall that the Unified theorem involves defining parabolas, ellipses, and hyperbolas by a single theorem involving just a focus and a directrix; this I will prove is in fact true in later videos so stay tuned! As explained in my earlier video, this theorem has the benefit of also being able to write a simple formula for conics in polar coordinates. In this particular video, I expand on the various variations of the resulting polar equations. The polar equations depend on where the directrix is located and I explain 4 different cases: x = +/- d and y = +/- d. The horizontal conics involve the cosine function, while the vertical conics involve the sine trigonometric function. This is a very important video in understanding the different variations of polar equations for conics and in understanding the need for this unified conics theorem, especially as I move further into the proof of the theorem; so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5lRmZoe0Rmx2yOxUQ
View video notes on the Hive blockchain: https://peakd.com/steemstem/@mes/shifted-conics-in-polar-coordinates-variations-in-polar-equations-theorem
Conics in Polar Coordinates: Unified Theorem for Conic Sections: https://youtu.be/eUvzyxCfJCw
Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Infinite Representations: https://youtu.be/QJYbnO7NzCk
Polar Coordinates: https://youtu.be/-KAdZL-N4ok .
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