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 a t 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

Answer: (D)

$\frac{27}{10}$

Answer 2

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 = $\frac{1}{2} .OA \times MN = \frac{27}{10} sq units$