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use implicit differentiation to find an equation of the tangent line to the curve at the given point.
9x^2+xy+9y^2=19, (1,1) (ellipse)

  • calculus -

    18x + y + xy' + 18yy' = 0
    y' = -(18x+y)/(x+18y)
    at (1,1) y' = -1
    so, the line is

    y-1 = -(x-1)

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