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Straight Lines and Pair of Straight Lines question

2025 · Shift 2 · Q20

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PYQ Library
JEE Advanced
Mathematics
Straight Lines and Pair of Straight Lines
2025 · Shift 2 · Q20

Straight Lines and Pair of Straight Lines question

2025 · Shift 2 · Q20

JEE AdvancedMathematicsStraight Lines and Pair of Straight LinesMCQ+3 / −1

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 \gt 0

, and parallel to the line

4x - \frac{3}{\sqrt{2}} y = 0

. Then the value of

pq

is :

A
$-6\sqrt{2}$
B
$-3\sqrt{2}$
C
$-9\sqrt{2}$
D
$-12\sqrt{2}$

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