Geo3.4

Find the area of the triangle formed by the lines $x^2+4xy+y^2=0,x+y=1\,$

The area of the triangle is $|\frac{n^2\sqrt{h^2-ab}}{am^2-2hlm+bl^2}|\,$

From the given equations $a=1,b=1,2h=4,l=1,m=1,n=-1\,$

Substituting the values in the formula, we get

The area is $|\frac{(-1)^2\sqrt{4-1}}{1(1^2)-4(1)(1)+1(1)^2}|\,$

$|\frac{\sqrt{3}}{-2}|\,$

$\frac{\sqrt{3}}{2}\,$ units.