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AP EAMCET202315 May 2023Morning ShiftMathematicsEllipseActual

Let x^2+y^2=20 be the director circle of an ellipse E whose major axis is X -axis and minor axis is Y -axis. If the length of the latus rectum of E is 2 , then the distance between its foci is

Options

  1. A4 5
  2. B4 3
  3. C4 2
  4. D3

Correct answer

B. 4 3

Step-by-step solution

Equation of director circle ellipse is x^2+y^2=a^2+b^2 a^2+b^2=20 Given that lotus rectum = 2 b^2 a =2 b^2=a from (i) and (ii) we get a=4 We have c^2=a^2-b^2=16-4=12 c=2 3 Distance between foci =2 c=4 3 .

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