## JoãoVitorMC 3 years ago translate and rotate the hyperbola 2 * x ^ 2 +6 * x * y +2 * y = 10 * (x + y +1)

1. JoãoVitorMC

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

4. experimentX

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

5. experimentX

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

6. JoãoVitorMC

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

7. experimentX

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

8. JoãoVitorMC

yes!

9. JoãoVitorMC

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

10. experimentX

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

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

12. JoãoVitorMC

ok xD

13. experimentX

I guess rotation first ... to eliminate the homogeneous form xy http://staff.argyll.epsb.ca/jreed/math30p/conics/standard.htm

14. experimentX

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

15. JoãoVitorMC

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

16. JoãoVitorMC

ok, i'll start rotating first

17. JoãoVitorMC

thanks a lot!

18. experimentX

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