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AP EAMCET202419 May 2024Evening ShiftMathematicsHyperbolaActual

If the product of eccentricities of the ellipse x^2 16 + y^2 b^2 =1 and the hyperbola x^2 9 - y^2 16 =-1 is 1 , then b^2=

Options

  1. A12 25
  2. B144
  3. C25
  4. D144 25

Correct answer

D. 144 25

Step-by-step solution

Given the ellipse x^2 16 + y^2 b^2 =1 and hyperbola aligned & x^2 9 - y^2 16 =-1 y^2 16 - x^2 9 =1 & eccentricity of ellipse = 1- b^2 16 & and eccentricity of hyperbola = 1+ 9 16 & Since, 1- b^2 16 1+ 9 16 =1 & 16-b^2= 16 16 25 b^2= 144 25 aligned

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