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## Homework Statement

Determine the equation of a tangent line to a curve at the given point.

3x

^{2}+xy+2y

^{2}=36 , P(2,3)

## Homework Equations

## The Attempt at a Solution

3x

^{2}+xy+2y

^{2}= 36

finding the derivatives of each term I get:

6x+xy'+y+4yy' = 0

xy'+4yy' = -6x-y

y'(x+4y) = -6x-y

[tex]y' = \frac{-6x-y}{x+4y}[/tex]

Which gives me a slope of 1.5 after plugging (2,3) in to the equation.

Then for the tangent: y-3=1.5(x-2) , y=1.5x

Somewhere I went wrong because this is not the right answer.