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NDA 1 2025 Maths, question 60

Topic: Analytical geometry

Q60

If any point on an ellipse is (3sin⁡α,5cos⁡α)\left( 3\sin\alpha,5\cos\alpha \right), then what is the eccentricity of the ellipse?

  1. (a) 4/34/3
  2. (b) 4/54/5Correct answer
  3. (c) 3/43/4
  4. (d) 1/21/2

Solution.

Answer: (b) 4/54/5

  1. Eliminating α\alpha gives x2/9+y2/25=1x^{2}/9 + y^{2}/25 = 1.
  2. Thus the semimajor axis is a=5a = 5 and the semiminor axis is b=3b = 3.
  3. The eccentricity is e=1−b2/a2=1−9/25=4/5e = \sqrt{1 - b^{2}/a^{2}} = \sqrt{1 - 9/25} = 4/5.