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NDA 2019 Maths · Mathematics · Conic Sections · medium

An ellipse whose major axis has length 10 and whose foci are 6 units apart has eccentricity 3/5. 2. The hyperbola (x^2/(4)-(y^2/(9)=-1 has its…

Single correct option

Consider the following statements:
1. An ellipse whose major axis has length 1010 and whose foci are 66 units apart has eccentricity 35\frac35.
2. The hyperbola x24−y29=−1\frac{x^2}{4}-\frac{y^2}{9}=-1 has its transverse axis along the y-axis.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

Statement 1: 2a=102a=10 and 2c=62c=6 give a=5a=5, c=3c=3, so e=ca=35e=\frac ca=\frac35; true. Statement 2: the equation is y29−x24=1\frac{y^2}{9}-\frac{x^2}{4}=1, whose positive term is in yy, so the transverse axis lies along the y-axis; true. Both statements are correct.
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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