Here's the question you clicked on:
calyne
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.
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...
wait so the x-intercepts are [+-]sqrt(3)?
well i got y' = -2x/(-1+2y)
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
check your derivative... again... i got something different
ok y' = (-2x+y)/(-x+2y) ?
so substituting (sqrt(3),0) m=2?
yep. notice you get the same thing for the other point... so they're parallel.