Use implicit differentiation to find an equation of the tangent line to the curve at the given point

Question

x^2+2xy+4y^2=12. Point (2,1). (Eclipse)

Answer 1

x^2+2xy+4y^2=12
2x + 2y + 2xy' + 8yy' = 0
(x+4y)y' = -x-y

y' = -(x+y)/(x+4y)
at (2,1) y' = -1/2

so, the line is

y-1 = -1/2 (x-2)

Answer 2

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