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NDA 2017 Maths · Mathematics · Conic Sections · medium

The angle between the asymptotes of the hyperbola x^2-3y^2=3 is

Single correct option

The angle between the asymptotes of the hyperbola x2−3y2=3x^2-3y^2=3 is
  1. A. 30∘30^\circ
  2. B. 90∘90^\circ
  3. C. 120∘120^\circ
  4. D. 60∘60^\circ
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Answer: (D) 60∘60^\circ

The hyperbola is x23−y2=1\frac{x^2}{3}-y^2=1 with a=3, b=1a=\sqrt3,\ b=1, so the asymptotes y=±x3y=\pm\frac{x}{\sqrt3} make angles ±30∘\pm30^\circ with the xx-axis and the angle between them is 2×30∘=60∘2\times30^\circ=60^\circ (containing the transverse axis). The value 30∘30^\circ is only half-angle, and 90∘90^\circ holds for rectangular hyperbolas only.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake