anonymous
  • anonymous
The equation x^2 - xy + y^2 = 3 represents a "rotated ellipse," that is, an ellipse whose axes are not parallel to the coordinate axes. Find the points at which this ellipse crosses the x-axis and show that the tangent lines at these points are parallel.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
to find the x-intercepts plug in y=0 and solve for x. to show that the tangent lines are parallel, plug in the coordinates of these points to the derivative y'. if they're parallel, they should have the same value...
anonymous
  • anonymous
wait so the x-intercepts are [+-]sqrt(3)?
anonymous
  • anonymous
yes

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anonymous
  • anonymous
well i got y' = -2x/(-1+2y)
anonymous
  • anonymous
so what, -2*sqrt(3)/(-1+0) = 2*sqrt(3), and then the same for -sqrt(3)..? what's that then? -2*-sqrt(3)/(-1+0) = -2sqrt3 i don't get it
anonymous
  • anonymous
check your derivative... again... i got something different
anonymous
  • anonymous
oh right crap
anonymous
  • anonymous
ok y' = (-2x+y)/(-x+2y) ?
anonymous
  • anonymous
that's what i got..
anonymous
  • anonymous
so substituting (sqrt(3),0) m=2?
anonymous
  • anonymous
yep. notice you get the same thing for the other point... so they're parallel.
anonymous
  • anonymous
yup. gotcha. thanks
anonymous
  • anonymous
yw

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