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JEE Advanced2009MathematicsEllipseActual

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2+9 y^2=9 meets its auxiliary circle at the point M . Then, the area of the triangle with vertices at A, M and the origin O is

Options

  1. A31 10
  2. B29 10
  3. C21 10
  4. D27 10

Correct answer

D. 27 10

Step-by-step solution

Equation of auxiliary circle is x^2+y^2=9 Equation of A M is x 3 + y 1 =1 On solving Eqs. (i) and (ii), we get Coordinates of M= (- 12 5 , 9 5 ) Now, area of A O M= 1 2 O A M N= 27 10 sq units

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