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COMEDK20269 May 2026Morning ShiftMathematicsHyperbolaActual

The difference between the distance of any point on the hyperbola from the two foci is 16 and the eccentricity is 2 . Then the equation of the hyperbola is

Options

  1. Ax^2 64 - y^2 192 = 1
  2. Bx^2 64 - y^2 256 = 1
  3. Cx^2 64 - y^2 64 = 1
  4. Dx^2 192 - y^2 64 = 1

Correct answer

A. x^2 64 - y^2 192 = 1

Step-by-step solution

The difference between the distances of any point on a hyperbola from its two foci is equal to the length of the transverse axis, which is 2a . Given 2a = 16 , which gives a = 8 . The eccentricity is given as e = 2 . For a hyperbola, the relation between a , b , and e is b^2 = a^2(e^2 - 1) . Substituting the values of a and e : b^2 = 8^2(2^2 - 1) b^2 = 64(4 - 1) = 64 3 = 192 The standard equation of the hyperbola is x^2 a^2 - y^2 b^2 = 1 . Substituting a^2 = 64 and b^2 = 192 , we get: x^2 64 - y^2 192 = 1 Answer: x

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