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Math Help - Equation of the normal line

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    Equation of the normal line

    Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2+xy-y^2=1 at a point (2,3)

    I don't even know how to start this I need step by step help if possible,
    Last edited by kristin08; May 1st 2009 at 05:43 PM.
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    Quote Originally Posted by kristin08 View Post
    Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2=xy-y^=1 at a point (2,3)

    I don't even know how to start this I need step by step help if possible,
    fix your equation ... you have two equal signs.
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    Sorry
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    Quote Originally Posted by kristin08 View Post
    Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2+xy-y^2=1 at a point (2,3)
    derivative ...

    2x + xy' + y - 2yy' = 0

    xy' - 2yy' = -2x - y

    y'(x - 2y) = -(2x+y)

    y' = \frac{2x+y}{2y-x}

    sub in the coordinates (2,3) ...

    y' = \frac{7}{4}

    normal slope is -\frac{4}{7}

    equation of the normal line is ...

    y - 3 = -\frac{4}{7}(x - 2)
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