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NDA 2025 Maths · Mathematics · Conic Sections · medium

The distance between the foci of an ellipse with major axis 10 and minor axis 8 is

Single correct option

The distance between the foci of an ellipse with major axis 1010 and minor axis 88 is
  1. A. 33
  2. B. 2412\sqrt{41}
  3. C. 1818
  4. D. 66
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Answer: (D) 66

The semi-axes are a=5a=5 and b=4b=4, so c=a2−b2=25−16=3c=\sqrt{a^2-b^2}=\sqrt{25-16}=3. The foci are 2c=62c=6 apart. The value 33 is only cc, 2412\sqrt{41} comes from using a2+b2\sqrt{a^2+b^2} (the hyperbola relation), and 1818 is 2(a+b)2(a+b).
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Original question written in the NDA 2025 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