2

In this video I go over further into Hyperbolas and this time determine the foci, asymptotes, and vertices of the hyperbola 9x^{2} – 16y^{2} = 144. This particular hyperbola is not written in “standard form”, which is the form x^{2}/a^{2} – y^{2}/b^{2} = 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 x^{2}/4^{2} – y^{2}/3^{2} = 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

Related Videos:

Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U

Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE

Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M

Hyperbola - Definition and derivation of the equation: x^{2}/a^{2} - y^{2}/b^{2} = 1: http://youtu.be/Y6iYC4VEAi0

Hyperbola Examples: http://youtu.be/LvccUMFrY3k .

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