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JEE Main201912 Jan 2019Evening ShiftMathematicsEllipseActual

Let S and S ' be the foci of an ellipse and B be any one of the extremities of its minor axis. If Δ S ' B S is a right angled triangle with right angle at B and area Δ S ' B S = 8 sq . units , then the length of a latus rectum of the ellipse is :

Options

  1. A2 2
  2. B2
  3. C4
  4. D4 2

Correct answer

C. 4

Step-by-step solution

Given that, ∠ S B S ' = π 2 ⇒ ∠ O B S = π 4 ⇒ b = a e     . . . i Also, area ∆ S B S ' = 8 ⇒ 1 2 . 2 a e . b = 8 ⇒ a e b = 8     . . . i i From equations i   &   i i , b 2 = 8 and a 2 = b 2 + a 2 e 2 = 8 + 8 = 16 ⇒ b = 2 2 and a = 4 Thus, the length of the latus rectum is 2 b 2 a = 16 4 = 4

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