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The line passing through the extremity A...

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 is auxiliary circle at the point `Mdot` Then the area of the triangle with vertices at `A ,M ,` and `O` (the origin) is (a) 31/10 (b) 29/10 (c) 21/10 (d) 27/10

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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