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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)

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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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