Since three lines x−3y=p, ax+2y=q and ax+y=r form a right angled triangle ∴ product of slopes of any two lines =−1 Suppose ax+2y=q and x−3y=p are ⟂ to each other. ∴
−a
2
×
1
3
=−1⇒a=6 Now, consider option one by one a=6 satisfies only option (a) ∴ Required answer is a2−9a+18=0