Conics in Polar Coordinates: Example 3: Hyperbola

Math Easy Solutions

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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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5sK1cp-4X1eVV1s7w

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conics-in-polar-coordinates-example-4-hyperbola