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COMEDK202510 May 2025Evening ShiftMathematicsHyperbolaActual

The length of the latus rectum of a conic 49 y^2-16 x^2=784 is

Options

  1. A7 2
  2. B49 2
  3. C49 2
  4. D7 2

Correct answer

B. 49 2

Step-by-step solution

The given equation of the conic is 49y^2 - 16x^2 = 784 . Dividing both sides by 784 , we get: 49y^2 784 - 16x^2 784 = 1 y^2 16 - x^2 49 = 1 This is the equation of a hyperbola of the form y^2 a^2 - x^2 b^2 = 1 , where a^2 = 16 and b^2 = 49 . The length of the latus rectum of a hyperbola y^2 a^2 - x^2 b^2 = 1 is given by the formula L = 2b^2 a . Here, a = 16 = 4 and b^2 = 49 . Substituting these values into the formula: L = 2 49 4 = 49 2 . Answer: 49 2

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