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If the eccentricity and the length of the latus rectum of an ellipse x 2 a 2 + y 2 b 2 = 1 are 3 2 and 1 respectively, then the sum of the lengths of major axis and minor axis of the ellipse is

Options

  1. A6
  2. B3
  3. C10
  4. D8

Correct answer

A. 6

Step-by-step solution

Given, Equation of ellipse x 2 a 2 + y 2 b 2 = 1 , eccentricity e = 3 2 and length of latusrectum 2 b 2 a = 1   . . . . . . . . . . . 1 Now we know that formula of eccentricity b 2 = a 2 1 - e 2 so by using this we get b 2 a 2 = 1 - 3 4 = 1 4   . . . . . . . . 2 Now by solving equation 1   &   2 we get, a = 2   &   b = 1 So sum of major axis and minor axis will be 4 + 2 = 6 .

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