<s>[INST] To prove triangle is equilateral> given one equation and one combined equation. show that the lines $ x^2 - 4xy +y^2 $ and $x +y=3 $ form an equilateral trinagle . Also Find Area.
Here is what I have tried:
$ l1 =x+y=3 $
The combined equation is:
$ x^2 - 4xy + y^2 $
compare it with general formula :
$ ax^2 +2hxy+y^2  $
What to do next ? 
I could find the slope but how will that help ?
 [/INST] If the angle between $y=mx$ and $x+y=3\iff y=-x+3$ is $60^\circ,$
$$\left|\frac{m-(-1)}{1+m(-1)}\right|=\tan60^\circ=\sqrt3$$
$$\iff\frac{m+1}{m-1}=\pm\sqrt3\iff(m+1)^2=3(m-1)^2\iff m^2-4m+1=0$$
Setting $m=\dfrac yx\implies y^2-4xy+x^2=0$
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