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If a and c are positive real numbers and the ellipse x^2 4 c^2 + y^2 c^2 =1 has four distinct points ir common with the circle x^2+y^2=9 a^2 , then

Options

  1. A9 a c-9 a^2-2 c^2 < 0
  2. B6 a c+9 a^2-2 c^2 < 0
  3. C9 a c-9 a^2-2 c^2>0
  4. D6 a c+9 a^2-2 c^2>0

Correct answer

C. 9 a c-9 a^2-2 c^2>0

Step-by-step solution

Radius =3 a Length of major axis =4 c Now, (Radius ) 9 a c-4 c^2 aligned 9 a c-9 a^2-2 c^2>9 a c-6 c^2 Again 3 a 0

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