yuki
  • yuki
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.
Mathematics
katieb
  • katieb
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yuki
  • yuki
\[2x^2+2\sqrt(3)xy-y^2+4x-y = 10\]
anonymous
  • 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
amistre64
  • amistre64
rotate it back lol

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yuki
  • yuki
uzma, it is actually \[H^2 - 4AB\]
yuki
  • yuki
its the same as the discriminant of a quadratic
anonymous
  • 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
yuki
  • yuki
oh, ok didn't see that well :/
anonymous
  • anonymous
A=2 B=-1 H=sqrt3 H^2-AB=3+2=5 so its ellipse
yuki
  • yuki
it's a hyperbola when it's positive :)
anonymous
  • anonymous
awwwww....u right:)
yuki
  • yuki
any one cares to find the angle of rotation needed to rotate it back ?
anonymous
  • anonymous
what does it actually mean?
yuki
  • yuki
ok my way of saying was vague
yuki
  • 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 \[Ax^2 + By^2 +Dx+Ey +F = 0\]
yuki
  • yuki
becomes my conic where x' = xcos(a) + ysin(a) y' = -xsin(a) + ycos(a) a is my angle of rotation
anonymous
  • anonymous
ah..rotation of axes :)
anonymous
  • anonymous
so u mean to transform the eq in the new system so that there isnt a mixed term?

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