If the lines x^2-4 x y+y^2=0 and x+y=10 contain the sides of an equilateral triangle, then the area of equilateral triangle is

Step-by-step solution

x^2-4 x y+y^2=0 aligned & = ⁻¹ ( 2 h ^2- ab a + b ) & = ⁻¹ ( 2 2^2-1 1 1+1 ) & = ⁻¹( 3 )=60^ aligned OM = |0+0-10| 1^2+1^2 =5 2 30^ = MB OM = MB 5 2 aligned & 1 3 = MB 5 2 & MB = 5 2 3 & AB =2 MB = 10 2 3 aligned Now area ( OAB )= 1 2 AB OM = 1 2 10 2 3 5 2 = 50 3