## yuki 5 years ago Do you guys want to solve a fun problem? Find the angle of rotation that is needed for the following conic and find out the type.

1. Yuki

$2x^2+2\sqrt(3)xy-y^2+4x-y = 10$

2. anonymous

the type of conic is determined by the sign of H^2-AB, where H=coefficient of xy A=coeff of x^2 B=coeff of y^2

3. amistre64

rotate it back lol

4. Yuki

uzma, it is actually $H^2 - 4AB$

5. Yuki

its the same as the discriminant of a quadratic

6. anonymous

it is also H^2-AB the difference is that in ur case H is coefficient of xy in the second case it is the coefficient of 2xy

7. Yuki

oh, ok didn't see that well :/

8. anonymous

A=2 B=-1 H=sqrt3 H^2-AB=3+2=5 so its ellipse

9. Yuki

it's a hyperbola when it's positive :)

10. anonymous

awwwww....u right:)

11. Yuki

any one cares to find the angle of rotation needed to rotate it back ?

12. anonymous

what does it actually mean?

13. Yuki

ok my way of saying was vague

14. Yuki

whenever the xy term has a coefficient other than 0 you can rotate the xy-coordinate system to make the equation have no xy term so that $Ax^2 + By^2 +Dx+Ey +F = 0$

15. Yuki

becomes my conic where x' = xcos(a) + ysin(a) y' = -xsin(a) + ycos(a) a is my angle of rotation

16. anonymous

ah..rotation of axes :)

17. anonymous

so u mean to transform the eq in the new system so that there isnt a mixed term?