Conics in Polar Coordinates: Example 1: Parabola
In this video I go over further into conic sections in polar coordinates and this time go over a simple example on determining the polar equation of a parabola. The example only gives the directrix line at y = -6 and that the focus is located at the origin. This is in fact all that we need to determine the parabola formula as well as to graph it. Recall that since the directrix is a horizontal line we use the polar equation that includes the sine function. Also since the directrix is at a negative distance from the origin/focus, the resulting polar equation is just r = 6/(1 – sin θ). To understand how I got to the polar equation and the unified theorem in general, make sure to watch my extensive derivation videos. This is a quick and simple illustration on determining the polar equation of a parabola so make sure to watch this video!
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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: Unified Theorem: Parabola Proof:
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