Conic Sections: Hyperbolas: Example 1

over 3 years ago (Edited)

In this video I go over further into Hyperbolas and this time determine the foci, asymptotes, and vertices of the hyperbola 9x² – 16y² = 144. This particular hyperbola is not written in “standard form”, which is the form x²/a² – y²/b² = 1 and which I derived in my earlier Conic Sections video. But we can get it in standard from by simply dividing both sides of the equation by 144 and then simplifying the resulting fractions. Doing so, I show that the hyperbola in standard form is x²/4² – y²/3² = 1. Thus, as shown also in my earlier derivation video, the foci are located at (+/- c, 0) = (+/- 5, 0); vertices at (+/- a, 0) = (+/- 4, 0), and asymptotes y = +/- (b/a)x = +/- (3/4)x. Graphing this using the amazing Desmos graphing calculator confirms that it a typical horizontal hyperbola, as expected. This is a very useful illustrating on walking through the steps in analyzing a hyperbola by first converting it into standard form and then graphing; so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5MfEMYv-svSfjLUCg

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conic-sections-hyperbolas-example-1