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JEE Main 2024 Mathematics question

MathematicsHyperbolaJEE Main 2024

Let P be a point on the hyperbola H : x²/9 − y²/4 = 1, in the first quadrant such that the area of triangle formed by P and the two foci of H is 2√13. Then, the square of the distance of P from the origin is

Answer: (A)

Solution

e = √(1 + 4/9) = √13/3, so the foci are (±√13, 0). The area of the triangle with base 2√13 and height β is ½ × 2√13

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Question ID VK-017000