Shifted Conics: Example 4: Hyperbola

in Threespeaklast month

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In this video I go over further into shifted conic sections and this time go into extreme detail in sketching the conic 9x2 – 4y2 – 72x + 8y + 176 = 0. While this formula is complicated, I show that we can simplify it by using algebra to gather all the terms with the x and y variable separately. Then I show that we can Complete the Square multiple times to only get the x and y variables to show up once. Doing so, we get a formula for a Vertical Shifted Hyperbola. This just means that we can take the basic formula for a vertical hyperbola, as well as all its foci, vertices, and asymptotes, and then shift them all according to the same methodology I covered in my earlier videos on shifted conics. While this is a VERY extensive video, the basic concept of shifting is quite simple, so this is a great video to illustrate shifting the more complicated hyperbola conic sections; so make sure to watch this video!

Download the notes in my video:!As32ynv0LoaIh5h95cN1ZmADqYxy6w

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Related Videos:

Shifted Conics: Example 3: Ellipse:
Shifted Conics: Example 2: Horizontal Parabola:
Shifted Conics: Example 1: Parabola:
Shifted Conics: Hyperbolas:
Shifted Conics: Parabolas:
Shifted Conics: Ellipses (and Circles):
Conic Sections: Hyperbola: Definition and Formula:
Conic Sections: Parabolas: Definition and Formula:
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles):
Completing the Square: .


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I don’t always shift hyperbolas but when I do I make sure to shift its foci, vertices, and asymptotes lines too ;)

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