Vertical Tangent Lines to an Ellipse

[unf0r5ak3n]

Homework Statement

Consider the curve x^2+xy+y^2=27

Homework Equations

Find all points on the curve where the lines tangent to the curve are vertical

The Attempt at a Solution

I found dy/dy = (-2x-y)/x+2y)

and I think I found the equations of lines visually to be x=6 and x=-6 but I'm not sure how to show the work.

 

[micromass]

So you'll need to find what points on the curve satisfy x+2y=0...

 

[unf0r5ak3n]

oh wow i didnt realize that thanks