find derivative... really quick?

Question

x^2 +xy + y^2 = 27

I did this and got.. (-(2x + y))/(x+2y)

but i saw this same question on yahoo answers.. and the person said it's positive..
(2x+y)/(x+2y)
soo which is right?

Thanks!

then.. it asks determine whether the lines tangent to the curve at the x=intercepts of the curve are parallel.. show analysis that leads to your conclusion..

so i saw this
......
x-intercepts of the curve have x = 0, and hence gradient is given by:

dy / dx = (2*0 + y) / (2*y + 0) = y / 2y = 1/2.

This is the same for both intercepts, and so they are parallel.

can someone expand on this a bit?
Thanks!!

Answer 1

Differentiating both sides wrt x
2x + y + xdy/dx + 2y dy/dx = 0
(x + 2y) dy/dx = -(x + 2y)
dy/dx = - (x + 2y) / (x + 2y)
So with a minus

Answer 2

derivative, term by term, assuming y is a function of x:

2x + y + xy' + 2yy' = 0
xy' + 2yy' = -2x - y
(x + 2y)y' = -2x - y
y' = -(2x + y)/(x+2y)
so you're right.

Answer 3

x^2 +xy + y^2 = 27
2x +y +xy' +2yy' = 0
y'(x+2y) = -(2x+y)
y' = -(2x+y)/(x+2y)
You are right

Answer 4

(2x+y)/(x+2y)