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AP EAMCET2014MathematicsApplication of Derivatives

If the curves x^2 a^2 + y^2 b^2 =1 and x^2 25 + y^2 16 =1 cut each other orthogonally, then a^2-b^2 equals to

Options

  1. A9
  2. B400
  3. C75
  4. D41

Correct answer

A. 9

Step-by-step solution

We know, two curves x^2 a₁^2 + y^2 b₁^2 =1 and x^2 a₂^2 + y^2 b₂^2 =1 cut orthogonally. Then, a₁^2-a₂^2=b₁^2-b₂^2 Here, equation of curves are x^2 a^2 + y^2 b^2 =1 and x^2 25 + y^2 16 =1 Condition of orthogonally, aligned & a^2-25=b^2-16 & a^2-b^2=25-16 & a^2-b^2=9 aligned

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