The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 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

Question

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 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) (31/10) (B) (29/10) (C) (21/10) (D) (27/10)

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Equation of auxiliary circle is x2+y2=9 ....(i) Equation of A M is (x/3)+(y/1)=1.....(ii) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3939eda0154776a49500043ffaa8bcc1-.png" /> On solving Eqs. (i) and (ii), we get M(-(12/5), (9/5)). Now, area of triangle A O M=(1/2) ⋅ O A × M N=(27/10) sq units

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

$\frac{31}{10}$

$\frac{29}{10}$

$\frac{21}{10}$

$\frac{27}{10}$

Equation of auxiliary circle is
$x^{2} + y^{2} = 9....$ (i)
Equation of $A M$ is $\frac{x}{3} + \frac{y}{1} = 1.....$ (ii)

On solving Eqs. (i) and (ii), we get $M (- \frac{12}{5}, \frac{9}{5})$ .
Now, area of $△ A OM = \frac{1}{2} \cdot O A \times MN = \frac{27}{10}$ sq units

Q. The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2+9y2=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

1031​

1029​

1021​

1027​