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AP EAMCET202423 May 2024Morning ShiftMathematicsHyperbolaActual

The area of the quadrilateral formed with the foci of the hyperbola x^2 16 - y^2 9 =1 and its conjugate hyperbola is (in square units)

Options

  1. A24
  2. B16
  3. C25
  4. D50

Correct answer

D. 50

Step-by-step solution

Hyperbola : x^2 16 - y^2 9 =1 e₁= 1+ 9 16 = 5 4 Conjugate hyperbola : x^2 9 - y^2 16 =1 e₂= 1+ 16 9 = 5 3 e₂ e₁ Area of quadrilateral =2 (a^2+b^2 )=2(16+9)=50 .

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