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The line passing through the " extremity...

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 integer closest to 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`

Text Solution

Verified by Experts


The equation AM is x+3y-3=0
Perpendicualr distacne of line from the origin `=(3)/(sqrt(10))=OB`
Length of `AM=2sqrt((9-(9)/(10))=2xx(9)/(sqrt(10))`
`:. "Area of" DeltaOAM=(1)/(2)xx2xx(9)/(sqrt(10))xx(3)/(sqrt(10))=(27)/(10)` sq. units
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