If the slope of one of the pair of lines represented by 2 x^2+3 x y+K y^2=0 is 2 , then the angle between the pair of lines is

Step-by-step solution

aligned & 2 x^2+3 x y+k y^2=0 & 2 k x^2+ 3 k x y+y^2=0 ....(i) aligned Let slope of other line be m then two lines are y=2 x, y aligned & =m x & (y-m x)(y-2 x)=0 & 2 m x^2-(m+2) x y+y^2=0 ...(ii) aligned Comparing (i) and (ii) aligned & 2 m= 2 k and m+2= -3 k & 2 m m+2 = -2 3 m= -1 2 , k=-2 aligned So, angle between the lines is = | m₁-m₂ 1+m₁ m₂ |= | 2+ 1 2 1-1 |= = 2