A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is

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Correct answer: A. (a)For ellipse x^24+ y^23=1 a^2 = 4 ⇒ a = 2, b^2 = 3 ⇒ e^2 = a^2−b^2a^2 = 14 ⇒ e = 12 ∴ hyperbola is con-focal with ellipse ae = AE, where 2A = 2sinθ ⇒ 1 = AE ⇒ 1 = (sin θ) E where E = excentricity of hyperbola ∴ B^2 = A^2 (E^2 – 1) ⇒ B = cosθ So equation of hyperbola is x^2A^2− y^2B^2=1 x^2s i n^2θ− y^2c o s^2θ = 1

$A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3 x^{2} + 4 y^{2} = 12. Then its equation is$

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