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JoãoVitorMC

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

  • one year ago
  • one year ago

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

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

    • one year ago
  3. ademm37
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    will be how to think

    • one year ago
  4. experimentX
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    for translation x = X - h y = Y - k

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

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

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

    • one year ago
  8. JoãoVitorMC
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    yes!

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

    • one year ago
  10. experimentX
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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

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

    • one year ago
  12. JoãoVitorMC
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    ok xD

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

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

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

    • one year ago
  16. JoãoVitorMC
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    ok, i'll start rotating first

    • one year ago
  17. JoãoVitorMC
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    thanks a lot!

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

    • one year ago
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