1. ## Ellipse

The equation of the graphed ellipse in my problem is x^2-xy+y^2=3.
How can I demonstrate mathematically that the tangent lines to this ellipse at the two x-intercepts are parallel?

-I used implicit differentiation to get dy/dx=(y-2x)/(2y-x), but now that I have done so, I don't know how to continue.

2. ## Find intercepts

Find the x-intercepts by plugging y=0 into the original ellipse equation and solve for x (there will be two solutions). Plug these two points (remembering y=0) into your equation for y'; the results for y' should be the same for the two points, showing that the tangents are parallel.

--Kevin C.