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AP EAMCET20225 Jul 2022Morning ShiftMathematicsEllipseActual

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse x^2 a^2 + y^2 b^2 =1 is 90^ , then it eccentricity is

Options

  1. A1 / 2
  2. B1 / 4
  3. C1 / 3
  4. D1 / 2

Correct answer

D. 1 / 2

Step-by-step solution

Apply pythagoras theorem, in A S₁ S₂ (S₁ A )^2+ (A S₂ )^2= (S₁ S₂ )^2a^2+a^2=(2 a e)^2 2 a^2=4 a^2 e^2 e= 1 2

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