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NDA 1 2025 Maths, question 59

Topic: Analytical geometry

Q59

What is the distance between the two foci of the hyperbola 25x2−75y2=22525x^{2} - 75y^{2} = 225?

  1. (a) 232\sqrt{3} units
  2. (b) 434\sqrt{3} unitsCorrect answer
  3. (c) 6\sqrt{6} units
  4. (d) 262\sqrt{6} units

Solution.

Answer: (b) 434\sqrt{3} units

  1. Dividing by 225 gives x2/9−y2/3=1x^{2}/9 - y^{2}/3 = 1.
  2. Hence a2=9a^{2} = 9, b2=3b^{2} = 3 and c2=a2+b2=12c^{2} = a^{2} + b^{2} = 12.
  3. The foci are (±23,0)\left( \pm 2\sqrt{3},0 \right), so their separation is 2c=432c = 4\sqrt{3} units.