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NDA 2018 Maths · Mathematics · Straight Lines · hard

The combined equation of the asymptotes of the hyperbola (x^2/(4)-(y^2/(9)=1 is

Single correct option

The combined equation of the asymptotes of the hyperbola x24−y29=1\frac{x^2}{4}-\frac{y^2}{9}=1 is
  1. A. 9x2−4y2=09x^2-4y^2=0
  2. B. 4x2−9y2=04x^2-9y^2=0
  3. C. 9x2−4y2=369x^2-4y^2=36
  4. D. 9x2+4y2=09x^2+4y^2=0
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Answer: (A) 9x2−4y2=09x^2-4y^2=0

The asymptotes are obtained by replacing the right-hand side 1 by 0: x24−y29=0\frac{x^2}{4}-\frac{y^2}{9}=0, i.e. 9x2−4y2=09x^2-4y^2=0, which gives y=±32xy=\pm\frac32x. The option 4x2−9y2=04x^2-9y^2=0 has slopes ±23\pm\frac23, the swapped values.
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Original question written in the NDA 2018 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