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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       . . i ∴ Equation of A M is x 3 + y 1 = 1       . . . ii On solving Eqs. (i) and (ii), we get M - 12 5 , 9 5 Now, area of Δ A O M = 1 2 O A × M N = 27 10 sq units Hence, option (d) is correct.

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