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NDA2025MathematicsEllipseActual

If any point on an ellipse is (3 , 5 ) , then what is the eccentricity of the ellipse?

Options

  1. A4 3
  2. B4 5
  3. C3 4
  4. D1 2

Correct answer

B. 4 5

Step-by-step solution

Let x = 3 and y = 5 . x 3 = and y 5 = Squaring and adding both equations: x^2 9 + y^2 25 = ^2 + ^2 = 1 This represents an ellipse with a^2 = 9 and b^2 = 25 . Since b > a , the eccentricity e is given by a^2 = b^2(1 - e^2) . 9 = 25(1 - e^2) 1 - e^2 = 9 25 e^2 = 16 25 e = 4 5 Answer: 4 5

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