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Let S = x , y ∈ R 2 : y 2 1 + r - x 2 1 - r = 1 , where r ≠ ± 1 . Then S represents:

Options

  1. AAn ellipse whose eccentricity is 1 r + 1 , when r > 1 .
  2. BA hyperbola whose eccentricity is 2 r + 1 , when 0 < r < 1 .
  3. CAn ellipse whose eccentricity is 2 r + 1 , when r > 1
  4. DA hyperbola whose eccentricity is 2 1 - r , when 0 < r < 1

Correct answer

C. An ellipse whose eccentricity is 2 r + 1 , when r > 1

Step-by-step solution

Given y 2 1 + r - x 2 1 - r = 1 If r ∈ 0 , 1 then this curve is a hyperbola whose eccentricity is 1 + 1 - r 1 + r = 2 r + 1 . If r > 1 , then this curve is an ellipse whose eccentricity is 1 - r - 1 r + 1 = 2 r + 1 .

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