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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.
 2 years ago
 2 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.
 2 years ago
 2 years ago

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dpaIncBest ResponseYou've already chosen the best response.1
to 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...
 2 years ago

calyneBest ResponseYou've already chosen the best response.0
wait so the xintercepts are [+]sqrt(3)?
 2 years ago

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

calyneBest ResponseYou've already chosen the best response.0
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
 2 years ago

dpaIncBest ResponseYou've already chosen the best response.1
check your derivative... again... i got something different
 2 years ago

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

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

dpaIncBest ResponseYou've already chosen the best response.1
yep. notice you get the same thing for the other point... so they're parallel.
 2 years ago
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