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JoãoVitorMC

  • 2 years ago

translate and rotate the hyperbola 2 * x ^ 2 +6 * x * y +2 * y = 10 * (x + y +1)

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  1. JoãoVitorMC
    • 2 years ago
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    This is the Equation \[x ^{2} + 3*x*y -5*x -4*y -5 =0\]

  2. ademm37
    • 2 years ago
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    hyperbola equation== \[x^{2} \div a ^{2} - y^{2} \div b ^{2} =1\]

  3. ademm37
    • 2 years ago
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    will be how to think

  4. experimentX
    • 2 years ago
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    for translation x = X - h y = Y - k

  5. experimentX
    • 2 years ago
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    For rotation \[ x = X \cos \theta - Y \sin \theta \\ y = Y \cos \theta + X \sin \theta \]

  6. JoãoVitorMC
    • 2 years ago
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    ok, but what i do first? translate or rotate?

  7. experimentX
    • 2 years ago
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    do you want to reduce it to standard form?? \[ \frac {x^2}a - \frac {y^2} b = 1 \] ??

  8. JoãoVitorMC
    • 2 years ago
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    yes!

  9. JoãoVitorMC
    • 2 years ago
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    that's it, but to get this form i need to translate and rotate

  10. experimentX
    • 2 years ago
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    It's indeed a hyperbola i guess translation first http://www.wolframalpha.com/input/?i=plot+2+*+x+^+2+%2B6+*+x+*+y+%2B2+*+y+%3D+10+*+%28x+%2B+y+%2B1%29 then rotation

  11. experimentX
    • 2 years ago
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    Let me check first ... i'm not sure i haven't done this for very long time

  12. JoãoVitorMC
    • 2 years ago
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    ok xD

  13. experimentX
    • 2 years ago
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    I guess rotation first ... to eliminate the homogeneous form xy http://staff.argyll.epsb.ca/jreed/math30p/conics/standard.htm

  14. experimentX
    • 2 years ago
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    this is going to be long work !!! do you have some kind of software for this type of job??

  15. JoãoVitorMC
    • 2 years ago
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    i use woframalpha sometimes, but i'll need to do this by hand heheh

  16. JoãoVitorMC
    • 2 years ago
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    ok, i'll start rotating first

  17. JoãoVitorMC
    • 2 years ago
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    thanks a lot!

  18. experimentX
    • 2 years ago
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    best of luck ... when many terms are involved, my sight get worse ...

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