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Find two points on an ellpise that have horizontal tangent

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data

    The equation 5x^2 - 6xy + 5y^2 = 16 represents an ellipse.

    Determine two points on the ellipse at which the tangent is horizontal.

    2. Relevant equations

    3. The attempt at a solution

    I find the derivative of the equation:

    (-10x + 6y) / (-6x + 10y) = 0 iff -10x + 6y = 0, so x = (3/5)y.
    Then I sub x back into original equation and get y, I get y = +/- 1/(sqrt(2)), which is wrong.

    What did I do wrong?
  2. jcsd
  3. Feb 24, 2012 #2


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    Homework Helper

    This is correct...

    Something with the back substitution into the original equation.

  4. Feb 24, 2012 #3
    Got it, thanks.
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