Let $S$ denote the locus of the point of intersection of the pair of lines $4 x-3 y=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 $(0, q), q0$, and parallel to the line $4 x-\frac{3}{\sqrt{2}} y=0$. Then the value of $p q$ is [JEE Advanced 2025]

Question

Let $S$ denote the locus of the point of intersection of the pair of lines $4 x-3 y=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 $4 x-\frac{3}{\sqrt{2}} y=0$. Then the value of $p q$ is [JEE Advanced 2025]

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Let \(S\) denote the locus of the point of intersection of the pair of lines \(4 x-3 y=12 \alpha \) \(4 \alpha x+3 \alph…

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