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 $x^{2}+9 y^{2}=9$ 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) $\frac{31}{10}$
(b) $\frac{29}{10}$
(c) $\frac{21}{10}$
(d) $\frac{27}{10}$
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Solution:
- Equation of auxiliary circle is
On solving Eqs. (i) and (ii), we get $M-\frac{12}{5}, \frac{9}{5}$.
Now, area of $\triangle A O M=\frac{1}{2} \cdot O A \times M N=\frac{27}{10} sq$ units
