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Math Help - Finding a tangent line

  1. #1
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    Finding a tangent line

    I need to find the equation of the line tangent to the graph of 2x^2 +2xy-y^2=2 at the point (1,2)?
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  2. #2
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    Quote Originally Posted by chaddy View Post
    I need to find the equation of the line tangent to the graph of 2x^2 +2xy-y^2=2 at the point (1,2)?
    Use implicite derivation:

    2x^2 +2xy-y^2=2~\implies~4x+2(y+x \cdot y')-2y \cdot y'=0 Solve the last equation for y':

    4x+2y+2x \cdot y' - 2y \cdot y'=0~\iff~y'(2x-2y)=-4x-2y~\iff~ y' = \frac{-4x-2y}{2x-2y}  = -\frac{2x+y}{x-y}

    Now plug in the coordinates of the tangent point to calculate the slope of the tangent:

    y' = m = -\frac{2+2}{1-2}=4

    Use the point-slope-formula to calculate the equation of the tangent line:

    y-2=4(x-1)~\iff~\boxed{y=4x-2}
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