Name: Conic Sections: Hyperbolas: Example 2: Vertical Hyperbola
Uploaded: 2023-08-10T21:20:55+00:00
Duration: 9 min 31 s
Description: 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 h

2 years ago

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Conics conic sections hyperbola math example hyperbola example vertical hyperbola foci vertices graphing hyperbola calculus mathematics

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!

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Related Videos:

Conic Sections: Hyperbolas: Example 2: Vertical Hyperbola: https://youtu.be/zBNSTkoEzFI
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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