A hyperbola passes through the focus of the ellipse

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A hyperbola passes through the focus of the ellipse x225+y216=1\frac{x^2}{25} + \frac{y^2}{16} = 1. The transverse and conjugate axes of the hyperbola coincide with the major and minor axes of the ellipse, and the product of the eccentricities of the ellipse and hyperbola is 1. (1) the equation of hyperbola is x29−y216=1\frac{x^2}{9} - \frac{y^2}{16} = 1 (2) the equations of hyperbola is x29−y225=1\frac{x^2}{9} - \frac{y^2}{25} = 1 (3) focus of hyperbola is (5,0)(5, 0) (4) vertex of hyperbola is (53,0)(5\sqrt{3}, 0)

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