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For the hyperbola x^2-y^2-4 x+2 y+c=0 , if the focus is S(2+2 2 , k) and the directrix that is adjacent to S is x=2+ 2 , then c=

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

B. -1

Step-by-step solution

Given hyperbola aligned x^2-y^2-4 x+2 y+c & =0 (x-2)^2-(y-1)^2 & =3-c (x-2)^2 3-c - (y-1)^2 3-c & =1 aligned Focus of hyperbola is aligned x-2 & = (3-c)+(3-c) x-2 & = 6-2 c [ a e= (3-c)+(3-c) ] x & =2 6-2 c aligned Here, 2+ 6-2 c =2+2 2 6-2 c =2 2 6-2 c=8 c=-1

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