Mathematics - Straight Lines Question with Solution | TestHub

Since three lines $x-3y=p$, $ax+2y=q$ and $ax+y=r$ form a right angled triangle $\therefore$ product of slopes of any two lines $=-1$ Suppose $ax+2y=q$ and $x-3y=p$ are $\perp$ to each other. $$\therefore \frac{-a}{2}\times \frac{1}{3}=-1\Rightarrow a=6$$ Now, consider option one by one $a=6$ satisfies only option (a) $\therefore$ Required answer is $a^2-9a+18=0$