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Math Help - Tangent to the curve

  1. #1
    mx-
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    Tangent to the curve

    Consider the curve given by 2xy - \sqrt{x^2+y}=-23.
    Find the equation of the line tangent to the curve at the point (−2, 5)

    Thanks
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by mx- View Post
    Consider the curve given by 2xy - \sqrt{x^2+y}=-23.
    Find the equation of the line tangent to the curve at the point (−2, 5)

    Thanks
    Differentiating implicitly we get 2xy'+2y-\frac{1}{2}(x+2y)^{\frac{-1}{2}}\cdot(2x+y')=0 now using this we get y-5=f'(-2,5)(x+2) I will leave the evaluation of f'(-2,5) to you...plug it in and solve for y'
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