Straight Lines · JEE Advanced previous year questions

2025 1 question

1. Q42025 · 18 May 2025 · Paper 2

   Let $S$ denote the locus of the point of intersection of the pair of lines $$4x-3y=12\alpha ,$$ $$4\alpha x+3\alpha y=12,$$ where $\alpha$ varies over the set of non-zero real numbers. Let $T$ be the tangent to $S$ passing through the points $(p,0)$ and $(0,q)$, $q>0$, and parallel to the line $4x-\frac{3}{\sqrt{2}}y=0$. Then the value of $pq$ is

   1. A.$-6\sqrt{2}$
   2. B.$-3\sqrt{2}$
   3. C.$-9\sqrt{2}$
   4. D.$-12\sqrt{2}$
   Show answer

   Answer: A