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AP EAMCET20226 Jul 2022Morning ShiftMathematicsEllipseActual

If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity is

Options

  1. A3 4
  2. B3 4
  3. C1 4
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Let the equation of ellipse be x^2 a^2 + y^2 b^2 =1 Length of Latus rectum = 2 ~b ^2 a and length of minor axis =2 b aligned & 2 ~b ^2 a = b b ^2 a ^2 = 1 4 & e = 1- b ^2 a ^2 = 1- 1 4 = 3 2 aligned

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