In this video I go over another example on hyperbolas and this time determine the formula of a vertical hyperbola and its foci while being given just the vertices and its asymptote line. We know the hyperbola opens up vertically because the given vertices (0, +/-1) are on the y-axis. Applying the standard form of a vertical hyperbola y^2/a^2 – x^2/b^2 = 0, where the foci is (0 , +/- c), asymptotes are y = +/- (a/b)x, and c^2 = a^2 + b^2, we can rearrange the resulting formula to get an equation of the resulting vertical hyperbola. Given the asymptote line of y = 2x, the resulting foci are (0, +/- sqrt(5)/2) and the hyperbola is of the formula y^2 – 4x^2 = 1. This is a quick and useful video illustrating the steps in analyzing a vertical hyperbola so make sure to watch this video!
Download the notes in my video:
https://1drv.ms/b/s!As32ynv0LoaIh5MyH6zpUJ1fXDbiFgView video notes on the Hive blockchain:
https://peakd.com/mathematics/@mes/conic-sections-hyperbolas-example-2-vertical-hyperbolaRelated Videos:
Conic Sections: Hyperbolas: Example 2: Vertical Hyperbola:
https://youtu.be/zBNSTkoEzFIConic Sections: Hyperbola: Definition and Formula:
https://youtu.be/UBIHovXNV9UConic Sections: Parabolas: Definition and Formula:
https://youtu.be/kCJjXuuIqbEConic Sections: Ellipses: Definition and Derivation of Formula (Including Circles):
https://youtu.be/9dETsJ2tz_MHyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1:
http://youtu.be/Y6iYC4VEAi0Hyperbola Examples:
http://youtu.be/LvccUMFrY3k .
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