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AP EAMCET202315 May 2023Evening ShiftMathematicsEllipseActual

Let the length of the latus rectum of an ellipse x^2 a^2 + y^2 b^2 =1 be equal to the length of its semi-major axis. If the radius of its director circle is 3 and e is its eccentricity, then the length of its latus rectum is

Options

  1. A1 a
  2. B1 b
  3. C1 e
  4. D1 a b

Correct answer

C. 1 e

Step-by-step solution

Given equation of ellipse x^2 a^2 + y^2 b^2 =1 Length of latus rectum = 2 b^2 a =a 2 b^2=a^2...(i) and equation of director circle is x^2+y^2=a^2+b^2 x^2+y^2=3 b^2=( 3 b)^2 Since, 3 b= 3 b=1 a= 2 e= c a = a^2-b^2 a = b a = 1 2 Now 1. 1. R =a= 2 = 1 e

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