Question

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 at the point M. Then, the area (insqunits) of the triangle with vertices at A, M and the origin O is

• A. $\frac{31}{10}$
• B. $\frac{29}{10}$
• C. $\frac{21}{10}$
• D. $\frac{27}{10}$

Answer 1

The correct option is D

$\frac{27}{10}$

Equation of auxiliary circle is
$x^2+y^2=9$ ... (i)
Equation of AM is $\frac{x}{3}+\frac{y}{1}=1$ ...(ii)
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On solving Eqs. (i) and (ii), we get $M(-\frac{12}{5},\frac{9}{5})$.
Now, area of $\Delta AOM=\frac{1}{2}.OA\times MN=\frac{27}{10}squnits.$