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NDA 2 2025 Maths, question 65

Topic: Analytical geometry

Q65

What is the distance between the foci of the hyperbola x2−4y2=1x^{2}-4y^{2}=1?

  1. (a) 3\sqrt{3}
  2. (b) 5\sqrt{5}Correct answer
  3. (c) 232\sqrt{3}
  4. (d) 252\sqrt{5}

Solution.

Answer: (b) 5\sqrt{5}

  1. Write the hyperbola as x²/1−y²/(1/4)=1.
  2. Then c²=a²+b²=1+1/4=5/4.
  3. The distance between the two foci is 2c=√5.