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AP EAMCET202125 Aug 2021Morning ShiftMathematicsHyperbolaActual

If in a hyperbola, the distance between the foci is 10 and transverse axis has length 8, then the length of its latus rectum is

Options

  1. A9
  2. B9 2
  3. C32 3
  4. D64 3

Correct answer

B. 9 2

Step-by-step solution

Given, 2 a e=10 and 2 a=8 a e=5, a=4 In hyperbola, aligned & & (a e)^2 & =a^2+b^2 & & 25 & =16+b^2 & & b^2 & =9 aligned Length of latus rectum = 2 b^2 a = 2 9 4 = 9 2

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