Ellipse 2 Question 12

12. The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2+9y2=9 meets its auxiliary circle at the point M. Then, the area (insqunits) of the triangle with vertices at A,M and the origin O is

(2009)

(a) 3110

(b) 2910

(c) 2110

(d) 2710

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Solution:

  1. Equation of auxiliary circle is

On solving Eqs. (i) and (ii), we get M125,95.

Now, area of AOM=12OA×MN=2710sq units



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