Question

The pair of straight lines $x^2-4xy+y^2=0$ together with the line $x+y+4\sqrt{6}=0$ form a triangle which is

• A. right angled but not isosscles
• B. right isosceles
• C. scalene
• D. equilateral

Answer 1

The correct option is D equilateral

$x^2-4xy+y^2=0$
$\Rightarrow y^2-4xy+4x^2=3x^2$
$\Rightarrow (y-2x{)}^2=3x^2$
$\Rightarrow y=(2\pm \sqrt{3})x$
$\therefore \Delta$ formed by $L_1=0,L_2=0$ & $L_3=0$ is equilateral.