Conics in Polar Coordinates: Example 2: Ellipse

in Threespeaklast month

In this video I go over another example on Conics in Polar Coordinates and this time go over the conic given by the formula r = 10/(3 – 2cosθ). The first thing to do whenever we are given a polar equation of a conic is to re-write it in the standard conic equation form, r = e∙d/(1 – e∙cosθ). Thus in this case, we would divide by 3 on the top and bottom of the equation. Doing so we get the polar equation r = (10/3)/[1 – (2/3)cosθ]. Thus we can see that we have: eccentricity e = 2/3, the directrix x = -d = -5, and since e is less than 1, the conic is an ellipse. I also determine the vertices by setting the polar angle to 0 and π to obtain (10, 0) and (2, π) in polar coordinates. This is a very detailed video breaking down how to determine the properties and graphical illustration of a conic, so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conics-in-polar-coordinates-example-2-ellipse

Related Videos:

Conics in Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H4OJpJ2gslXVLT8mP-SgJP
Conics in Polar Coordinates: Unified Theorem: Ellipse Proof: https://youtu.be/HRFzk1vyLmg .

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I don’t always sketch an ellipse in polar coordinates but when I do I make sure to check the eccentricity, directrix, and the type of conic before I sketch it ;)

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conics-in-polar-coordinates-example-2-ellipse