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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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This is the Equation \[x ^{2} + 3*x*y -5*x -4*y -5 =0\]
hyperbola equation== \[x^{2} \div a ^{2} - y^{2} \div b ^{2} =1\]
will be how to think

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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?? \[ \frac {x^2}a - \frac {y^2} b = 1 \] ??
yes!
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
ok xD
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
thanks a lot!
best of luck ... when many terms are involved, my sight get worse ...

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