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NDA 2019 Maths · Mathematics · Conic Sections · easy

For the ellipse 4x^2+9y^2=144, the sum of the distances of any point on it from the two foci is

Single correct option

For the ellipse 4x2+9y2=1444x^2+9y^2=144, the sum of the distances of any point on it from the two foci is
  1. A. 66
  2. B. 454\sqrt5
  3. C. 1212
  4. D. 2424
Show answer and solution

Answer: (C) 1212

Writing x236+y216=1\frac{x^2}{36}+\frac{y^2}{16}=1 gives a=6a=6, b=4b=4. By the focal property of the ellipse the sum of focal distances is the constant 2a=122a=12. The value 66 is only the semi-major axis, and 45=2204\sqrt5=2\sqrt{20} is the distance between the foci 2c2c.
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Original question written in the NDA 2019 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