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The foci of the hyperbola 4 x^2-9 y^2-1=0 are

Options

  1. A( 13 , 0)
  2. B( 13 6 , 0 )
  3. C(0, 13 6 )
  4. DNone of the above

Correct answer

B. ( 13 6 , 0 )

Step-by-step solution

Standard equation of hyperbola x^2 a^2 - y^2 b^2 =1 with foci S(a e, 0) and S^ (-a e, 0) Given equation is 4 x^2-9 y^2=1 or, x^2 ( 1 4 ) - y^2 ( 1 9 ) =1 Here, a^2= 1 4 , b^2= 1 9 From hyperbola properties, or, aligned b^2 & =a^2 e^2-a^2 a^2 e^2 & =b^2+a^2 & = 1 9 + 1 4 = 13 36 aligned or, a e= 13 6 Hence, foci : ( 13 6 , 0 )

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