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AP EAMCET202319 May 2023Morning ShiftMathematicsHyperbolaActual

Let x+y+1=0 and x-y+4=0 be the asymptotes of a hyperbola H . If (1,1) is a point on H , then the length of the latus rectum of H is

Options

  1. A4 3
  2. B3
  3. C4 2
  4. D5

Correct answer

A. 4 3

Step-by-step solution

We know that, the a symptotes of hyperbola (x-h)^2 a^2 - (y-k)^2 b^2 =1 is (y-k)= b a (x-h) ... (i) and latus rectum is 2 b^2 a Rewrite the given a symptotes are aligned & (y- 3 2 )= 1 (x+ 5 2 ) b a =1 & (x+ 5 2 )^2 a^2 - (y- 3 2 )^2 b^2 =1 aligned Since b=a and hyperbola passes through (1,1) . Hence a^2= (1+ 5 2 )^2- (1- 3 2 )^2=12 Hence b^2=a^2=12 Therefore latus rectum =2 ( b^2 a )=2 ( 12 12 )=4 3

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