A hyperbola is centred at the origin

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

Problem

A hyperbola is centred at the origin, has vertices at (±4,0)(\pm4,0) and its asymptotes are y=±34xy=\pm\dfrac{3}{4}x. Which of the following is its equation? (a) y216−x29=1\dfrac{y^{2}}{16}-\dfrac{x^{2}}{9}=1 (b) x216+y29=1\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1 (c) x216−y29=1\dfrac{x^{2}}{16}-\dfrac{y^{2}}{9}=1 (d) x29−y216=1\dfrac{x^{2}}{9}-\dfrac{y^{2}}{16}=1

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