Conics in Polar Coordinates: Example 3: Hyperbola

In this video I go over another example on conic sections in polar coordinates and this time sketch a hyperbola in polar coordinates. The hyperbola is given by the formula r = 12/(2 + 4sinθ) which can be rewritten to r = 6/(1 + 2sinθ) to be in the standard conic form, r = e∙d(1 + e∙sinθ). Thus with an eccentricity e = 2, a directrix y = d = 3, and determining the vertices and x-intercepts we can graph the hyperbola. Also for more accuracy I show that the asymptote lines are parallel to the angles θ = 7π/6 and θ = - π/6. Later in the video I briefly mentioned about determining the exact polar equations of the asymptote lines, which will be a topic of further research so stay tuned! This is a great and extensive example on determining the properties of a conic in polar coordinates and manually sketching it in a step-by-step methodology; 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: Example 2: Ellipse: https://youtu.be/iMy9HN30yIo
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY .

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