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
- A12 25
- B144
- C25
- 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