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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Answer:

Correct Answer: 12. (d)

Solution:

  1. 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



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