Let O be the origin, and P and Q be two points on the rectangular hyperbola x y = 12 such that the mid point of the line segment PQ is (1/2, -1/2 ) . Then the area of the triangle OPQ equals:

Mathematics · Hyperbola

JEE Main 2026 — 2 April, Evening Shift — Question 33

Let O be the origin, and P and Q be two points on the rectangular hyperbola $\mathbf{x}\mathbf{y} = 12$ such that the mid point of the line segment PQ is $\left(\frac{1}{2}, -\frac{1}{2}\right)$ . Then the area of the triangle OPQ equals:

Option A:
$\frac{3}{2}$
Option B:
$\frac{5}{2}$
Option C:
$\frac{7}{2}$
Correct
Option D:
$\frac{9}{2}$

Answer: C

Step-by-step solution

Equation of chord whose midpoint is $\left(\frac{1}{2}, \frac{-1}{2}\right)$ $\frac{\mathrm{x}}{\mathrm{x}_{1}}+\frac{\mathrm{y}}{\mathrm{y}_{1}}=2$ $2 \mathrm{x}-2 \mathrm{y}=2$ $x-y=1$ solving with $\mathrm{xy}=12$ $\mathrm{P}(-3,-4), \mathrm{Q}(4,3)$ Area $(\triangle \mathrm{OPQ})=\frac{1}{2}|-3 \times 3-(-4)(4)|=\frac{7}{2}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 2 April, Evening Shift
Subject: Mathematics
Chapter: Hyperbola
Topic: Rectangular Hyperbola