The equation of straight line is, x2−(a+2)xy+y2+a(x+y−1)=0 …… (I) According to the question The equations of lines are (y−1)−tan‌θ(x−1)=0 And, (y−1)−cot‌θ(x−1)=0 Thus, the combined equation is, (y−1)2−(x−1)(y−1)[tan‌θ+cot‌θ]+(x−1)2=0 x2−
2
sin‌2‌θ
xy+y2+(
2
sin‌2‌θ
−2)(x+y−1)=0……(II) Compare equation (I) and (II). a+2=