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

Question

anonymous · Answer

This is the Equation
$$x ^{2} + 3*x*y -5*x -4*y -5 =0$$

anonymous · Answer

hyperbola equation==  $$x^{2} \div a ^{2} - y^{2} \div b ^{2} =1$$

anonymous · Answer

will be how to think

experimentx · Answer

for translation 
x = X - h
y = Y - k

experimentx · Answer

For rotation
$$ x = X \cos \theta - Y \sin \theta \ y = Y \cos \theta + X \sin \theta $$

anonymous · Answer

ok, but what i do first? translate or rotate?

experimentx · Answer

do you want to reduce it to standard form??
$$ \frac {x^2}a - \frac {y^2} b = 1 $$
??

anonymous · Answer

yes!

anonymous · Answer

that's it, but to get this form i need to translate and rotate

experimentx · Answer

experimentx · Answer

Let me check first ... i'm not sure 
i haven't done this for very long time

anonymous · Answer

ok xD

experimentx · Answer

experimentx · Answer

this is going to be long work !!! do you have some kind of software for this type of job??

anonymous · Answer

i use woframalpha sometimes, but i'll need to do this by hand heheh

anonymous · Answer

ok, i'll start rotating first

anonymous · Answer

thanks a lot!

experimentx · Answer

best of luck ... when many terms are involved, my sight get worse ...