The area (in sq. units) of the triangle formed by the lines x^2-3 x y+y^2=0 and x+y+1=0 , is

Step-by-step solution

Given equations of line are array r x^2-3 x y+y^2=0 x+y+1=0 array and x+y+1=0 Let, m₁ and m₂ be the slope of the line x^2-3 x y+y^2=2 . aligned m₁+m₂ & =- Coefficient of x y Coefficient of y^2 & =+ 3 1 =3 aligned and aligned m₁ m₂ & = Coefficient of x^2 Coefficient of y^2 & = 1 1 =1 aligned Now, aligned m₁-m₂ & = (m₁+m₂ )^2-4 m₁ m₂ & = (3)^2-4 1 & = 9-4 = 5 m₁-m₂ & = 5 aligned On solving Eqs. (i) and (iii), we get and aligned & m₁= 3+ 5 2 & m₂= 3- 5 2 aligned Equation of lines will be and aligned & y= 3+ 5 2 x & y=