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Math Help - Ellipse

  1. #1
    Junior Member
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    New York City
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    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.
    Last edited by blurain; December 5th 2007 at 08:52 PM.
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  2. #2
    Senior Member
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    Dec 2007
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    Anchorage, AK
    Posts
    276

    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.
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