The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $x^2 + 9y^2 = 9$ meets its auxiliary circle a t the point M.
Then, the area (insqunits) of the triangle with vertices at A, M and the origin O is
- $\frac{31}{10}$
- $\frac{29}{10}$
- $\frac{21}{10}$
- $\frac{27}{10}$
The Correct Option is D
Solution and Explanation
The correct option is(D): \( \frac{27}{10} \)
Equation of auxiliary circle is
\(x^2 + y^2 =9\)
Equation of AM is \(\frac{x}{3} +\frac{y}{1} = 1\)
on solving Eq s (i) and (ii) , we get \(M \bigg( -\frac{12}{5} , \frac{9}{5} \bigg) .\)
Now, area of A AOM = \(\frac{1}{2} .OA \times MN = \frac{27}{10} sq units\)
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