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Area of the triangle formed by a point on a hyperbola and its two foci

This type of question, asked 2 times: 30 Jan 2024, 22 Jan 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    30 Jan 2024

    160
    Let PP be a point on the hyperbola H:x29−y24=1H:\frac{x^{2}}{9}-\frac{y^{2}}{4}= 1, in the first quadrant such that the area of triangle formed by PP and the two foci of HH is 2132\sqrt{13}. Then, the square of the distance of PP from the origin is

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  2. Question 2

    22 Jan 2026 S2

    61
    Let P(10,215)P(10,2\sqrt{15}) be a point on the hyperbola x2a2−y2 b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{{\text{ }b}^{2}}= 1, whose foci are S and S′S^{'}. If the length of its latus rectum is 8 , then the square of the area of △PSS′\bigtriangleup PSS^{'} is equal to :

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