Given equation of pair of straight lines can be rewritten as
x(y−1)−1(y−1)=0 (x−1)(y−1)=0 x=1 y=1 The three concurrent lines are,
x=1.....(1) y=1.....(2) x+ay−3=0 since equation (1) and (2) intersect at only points namely (1,1)
therefore, this point also satisfy the equation (3)
1+a−3=0 a=2 Now the pair of line becomes,
2x2−13xy−7y2+x+23y−6=0 The acute angle between the lines is calculated as
tanθ=|| =|| =|−3| =3 The angle is calculated as,\
θ=tan−1(3) =cos−1()