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JEE Main202331 Jan 2023Evening ShiftMathematicsHyperbolaActual

Let H be the hyperbola, whose foci are 1 ± 2 , 0 and eccentricity is 2 . Then the length of its latus rectum is:

Options

  1. A3
  2. B5 2
  3. C2
  4. D3 2

Correct answer

C. 2

Step-by-step solution

Given the foci points of a hyperbola are 1 ± 2 , 0 So, S 1 + 2 , 0 , S ' 1 - 2 , 0 S S ' = 2 ae = ( 1 + 2 ) - ( 1 - 2 ) ⇒ 2 a e = 2 2 ⇒ 2 × a × 2 = 2 2 ,   given   e = 2 ⇒ a = 1 Since b 2 = a 2 ( e 2 - 1 ) ⇒ b 2 = 1 ( 2 - 1 ) = 1 So, the latus rectum of a hyperbola is given by, L.R. = 2 b 2 a L.R. = 2

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