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COMEDK2023Evening ShiftMathematicsEllipseActual

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

Options

  1. A1 2
  2. B2 2 3
  3. C1 3
  4. D2 3

Correct answer

B. 2 2 3

Step-by-step solution

Let the length of the major axis be 2a and the length of the minor axis be 2b . Given that the length of the major axis is 3 times the length of the minor axis, we have 2a = 3(2b) , which simplifies to a = 3b . The eccentricity e of an ellipse is given by the formula e = 1 - b^2 a^2 . Substituting a = 3b into the formula: e = 1 - b^2 (3b)^2 e = 1 - b^2 9b^2 e = 1 - 1 9 e = 8 9 e = 8 3 = 2 2 3 Answer: 2 2 3

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