Find the two horizontal and two vertical tangent lines of the equation x^2+xy+y^2=9.

Differentiating w.r.t y,
We get, 

2 x (d x/d y) + y (d x/d y) + x + 2 y = 0 

Put 
d x/d y = 0 

The equation becomes:
x=2 y 

substituting into main equation

We, get

3 y^2 =9 

y= √3

x = ± 2√3