If θ is acute angle between two lines x2+6xy+y2=0 then the value of 2sinθ+cosθ is

If θ is acute angle between pair of lines represented by the equation ax2+2hxy+by2=0 then cosθ=a+b(a−b)2+(2h)2For the equation x2+6xy+y2=0,a=1,h=3,b=1Hence, cosθ=26=13 Use the right triangle for sinθ=223Hence, 2sinθ+cosθ=2223+13=43+13=53Therefore, 2sinθ+cosθ=53