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NDA 2024 Maths · Mathematics · Conic Sections · easy

The length of the transverse axis of the hyperbola 9x^2-16y^2=144 is

Single correct option

The length of the transverse axis of the hyperbola 9x2−16y2=1449x^2-16y^2=144 is
  1. A. 44
  2. B. 88
  3. C. 66
  4. D. 1010
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Answer: (B) 88

Divide by 144: x216−y29=1\frac{x^2}{16}-\frac{y^2}{9}=1, so a2=16a^2=16 and b2=9b^2=9. The transverse axis lies along the xx-axis and has length 2a=82a=8. Trap: 4 is only aa, 6 is the conjugate axis 2b2b, and 10 is the distance between the foci, 2a2+b2=2252\sqrt{a^2+b^2}=2\sqrt{25}.
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