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JoãoVitorMC
translate and rotate the hyperbola 2 * x ^ 2 +6 * x * y +2 * y = 10 * (x + y +1)
This is the Equation \[x ^{2} + 3*x*y -5*x -4*y -5 =0\]
hyperbola equation== \[x^{2} \div a ^{2} - y^{2} \div b ^{2} =1\]
for translation x = X - h y = Y - k
For rotation \[ x = X \cos \theta - Y \sin \theta \\ y = Y \cos \theta + X \sin \theta \]
ok, but what i do first? translate or rotate?
do you want to reduce it to standard form?? \[ \frac {x^2}a - \frac {y^2} b = 1 \] ??
that's it, but to get this form i need to translate and rotate
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
Let me check first ... i'm not sure i haven't done this for very long time
I guess rotation first ... to eliminate the homogeneous form xy http://staff.argyll.epsb.ca/jreed/math30p/conics/standard.htm
this is going to be long work !!! do you have some kind of software for this type of job??
i use woframalpha sometimes, but i'll need to do this by hand heheh
ok, i'll start rotating first
best of luck ... when many terms are involved, my sight get worse ...