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 at the point m. Then the area of the triangle with vertices at a, m, and o (the origin) is

Answer 1

Answer:

Correct option is

C

10

27

The equation of ellipse is

9

x

2

+y

2

=1

The length of semi-major axis is a=3 and the length of semi-minor axis is b=1

The coordinates of point A is (3,0) and the coordinates of point B is (0,1)

The equation of line passing through A,B is x+3y=3

The equation of an auxiliary circle of an ellipse is x

2

+y

2

=9

The line AB cuts x

2

+y

2

=9 at point M

By solving the above equations

The coordinates of point M are (−

5

12

,

5

9

)

The area of triangle AMO is

2

1

∣0(0−

5

9

)+3(

5

9

−0)−

5

12

(0−0)∣=

10

27

solution