If is a double ordinate of the hyperbola such that is an equilateral triangle, where is the centre of the hyperbola, then which of the following is true?

Explanation: Concept Eccentricity : For the hyperbola , . Focus : . Parametric Point : Any point on the hyperbola can be represented as . Calculation The center of the hyperbola is . Let the coordinates of the double ordinate be and . Let be the point on the x-axis where the double ordinate intersects, so . In , given it is an equilateral triangle: and . In , , , and . Using trigonometry in right-angled : Since the maximum value of is less than (and for a hyperbola, , meaning cannot be as cannot be ): Correct Option: 2

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NIMCET 2014 — Mathematics PYQ

NIMCET | Mathematics | 2014

If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\triangle OPQ$ is an equilateral triangle, where $O$ is the centre of the hyperbola, then which of the following is true?

Choose the correct answer: