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anonymous
 4 years ago
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 xaxis and show that the tangent lines at these points are parallel.
anonymous
 4 years ago
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 xaxis and show that the tangent lines at these points are parallel.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0to find the xintercepts 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
 4 years ago
Best ResponseYou've already chosen the best response.0wait so the xintercepts are [+]sqrt(3)?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well i got y' = 2x/(1+2y)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so 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
 4 years ago
Best ResponseYou've already chosen the best response.0check your derivative... again... i got something different

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok y' = (2x+y)/(x+2y) ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so substituting (sqrt(3),0) m=2?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yep. notice you get the same thing for the other point... so they're parallel.
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