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If P x 1 ,   y 1 is a point on the ellipse b 2 x 2 +   a 2 y 2 = a 2 b 2 then the area of Δ S P S ′ =

Options

  1. Aa e a 2 - x 1 2
  2. Bb e b 2 - x 1 2
  3. Ca e b 2 - x 1 2
  4. Db e a 2 - x 1 2

Correct answer

D. b e a 2 - x 1 2

Step-by-step solution

x 2 a 2 + y 2 b 2 = 1 ⇒ y 1 2 b 2 = 1 - x 1 2 a 2 y 1 = b a a 2 - x 1 2 Δ S P S ′ = 1 2 × 2 a e × y 1 = a e × b a a 2 - x 1 2 Δ S P S ′ = b e a 2 - x 1 2

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