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NDA 2017 Maths · Mathematics · Conic Sections · hard

The distance between the directrices of the ellipse (x^2/(25)+(y^2/(9)=1 is

Single correct option

The distance between the directrices of the ellipse x225+y29=1\frac{x^2}{25}+\frac{y^2}{9}=1 is
  1. A. 254\frac{25}{4}
  2. B. 252\frac{25}{2}
  3. C. 1010
  4. D. 88
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Answer: (B) 252\frac{25}{2}

a=5, b=3a=5,\ b=3, so e=1−925=45e=\sqrt{1-\frac{9}{25}}=\frac45. The directrices are x=±ae=±254x=\pm\frac{a}{e}=\pm\frac{25}{4}, so their distance apart is 252\frac{25}{2}. The value 254\frac{25}{4} is only the distance of one directrix from the centre; 1010 is the major axis and 88 is the distance between the foci.
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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