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 of the triangle with vertices at $A,\ M$ and the origin $O$ is

Question

Dr. Abubacker · Accepted Answer

(d)
Equation of auxiliary circle is
$x^{2} + y^{2} = 9\ \ \ldots(i)$
[image:11_image79.emf]
Equation of $AM$ is $\frac{x}{3} + \frac{y}{1} = 1\ \ \ldots\ (ii)$
On solving Eqs. (i) and (ii) , we get $M\left( - \frac{12}{5},\frac{9}{5} ight)$
Now, area of $\mathrm{\Delta}AOM = \frac{1}{2}.OA 	imes MN$
$= \frac{27}{10}\ sq\ unit\$

Q. 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 of the triangle with vertices at $A,\ M$ and the origin $O$ is

Explanation

Reviewed by Dr. Abubacker

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