Given the curve $\displaystyle x^2+xy+y^2=9$

a) Find $\displaystyle y'$

$\displaystyle x^2+xy+y^2=9$

Taking the derivative of the above equation and using product rule for xy, i get,

$\displaystyle 2x+(y+xyy')+2yy' = 0$

$\displaystyle xy'+2yy' = -2x-y$

$\displaystyle y'(x-2y)=-2x-y$

Answer:

$\displaystyle y' = (-2x-y)/(x+2y)$

b) Find all points on the curve at which the tangent line is horizontal

Is a) correct? and also how do i do letter b)? i have no clue what to do. thanks!