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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.
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.

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Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1\[2x^2+2\sqrt(3)xyy^2+4xy = 10\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the type of conic is determined by the sign of H^2AB, where H=coefficient of xy A=coeff of x^2 B=coeff of y^2

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1uzma, it is actually \[H^2  4AB\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1its the same as the discriminant of a quadratic

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is also H^2AB the difference is that in ur case H is coefficient of xy in the second case it is the coefficient of 2xy

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1oh, ok didn't see that well :/

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0A=2 B=1 H=sqrt3 H^2AB=3+2=5 so its ellipse

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1it's a hyperbola when it's positive :)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1any one cares to find the angle of rotation needed to rotate it back ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what does it actually mean?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1ok my way of saying was vague

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1whenever the xy term has a coefficient other than 0 you can rotate the xycoordinate system to make the equation have no xy term so that \[Ax^2 + By^2 +Dx+Ey +F = 0\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1becomes my conic where x' = xcos(a) + ysin(a) y' = xsin(a) + ycos(a) a is my angle of rotation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ah..rotation of axes :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so u mean to transform the eq in the new system so that there isnt a mixed term?
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