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The line passing through the extremity A...

The line passing through the extremity `A` of the major exis 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 correct Answer is:
D
Equations of auxilary circle is
`x^(2)+y^(2)=9`
Euations of AM is `(x)/(3)+(y)/(1)=1`

On solving Eqs.(i) and (ii) we get M`(-(12)/(5),(9),(5))`
Now , area of `Delta APOM =(1)/(2) OAxxMN=(27)/(10) `sq units.
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