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

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

Tardigrade Admin · Accepted Answer

Equation of line AM is x+3 y-3=0 Perpendicular distance of line from origin =(3/√10) Length of AM =2 √9-(9/10)=2 × (9/√10) ⇒ Area =(1/2) × 2 × (9/√10) × (3/√10)=(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 at the point $M$ . Then the area 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 line AM is $x + 3 y - 3 = 0$
Perpendicular distance of line from origin $= \frac{3}{10}$
Length of $A M = 2 9 - \frac{9}{10} = 2 \times \frac{9}{10}$
$\Rightarrow$ Area $= \frac{1}{2} \times 2 \times \frac{9}{10} \times \frac{3}{10} = \frac{27}{10}$ 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 at the point M. Then the area of the triangle with vertices at A,M and the origin O is

1031​

1029​

1021​

1027​