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AP EAMCET201921 Apr 2019Evening ShiftMathematicsEllipseActual

Let P be any point on the ellipse 7 x 2 + 16 y 2 = 112 , S be a focus, L be the corresponding directrix and P M be the perpendicular distance from P to directrix L . Then S P P M =

Options

  1. A1 4
  2. B1 2
  3. C3 4
  4. D1 2

Correct answer

C. 3 4

Step-by-step solution

We have, the given equation of an ellipse is 7 x 2 + 16 y 2 = 112 . ⇒ x 2 16 + y 2 7 = 1 The eccentricity of the ellipse is, e = 1 - 7 16 = 9 16 = 3 4 ∴   S P P M = e ⇒ S P P M = 3 4

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