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: https://1drv.ms/b/s!As32ynv0LoaIh5h95cN1ZmADqYxy6w

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-example-4-hyperbola

Related Videos:

Shifted Conics: Example 3: Ellipse: https://youtu.be/RwSyIKOnoHE
Shifted Conics: Example 2: Horizontal Parabola: https://youtu.be/v6tbsCCQNp0
Shifted Conics: Example 1: Parabola: https://youtu.be/VqxlOUqzvGY
Shifted Conics: Hyperbolas: https://youtu.be/Evz6duQ2-U8
Shifted Conics: Parabolas: https://youtu.be/UlrAkAW3T8Y
Shifted Conics: Ellipses (and Circles): https://youtu.be/ZqtUfaQbj7U
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
Completing the Square: http://youtu.be/5uxV6-f_qc0 .


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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 ;)

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-example-4-hyperbola