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MathsJEE Main 23 Jan 2026, Shift 2·Q9·MCQ·Moderate

Conic Sections · Hyperbola chord and eccentricity

Let PQPQ be a chord of the hyperbola x24−y2b2=1\dfrac{x^2}{4} - \dfrac{y^2}{b^2} = 1, perpendicular to the xx-axis such that OPQOPQ is an equilateral triangle, OO being the centre of the hyperbola. If the eccentricity of the hyperbola is 3\sqrt3, then the area of the triangle OPQOPQ is:
  1. (1)232\sqrt3
  2. (2)835\dfrac{8\sqrt3}{5}
  3. (3)115\dfrac{11}{5}
  4. (4)95\dfrac{9}{5}

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