Question

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 31/10 (b) 29/10 (c) 21/10 (d) 27/10
A. `(31)/(10)`
B. `(29)/(10)`
C. `(21)/(10)`
D. `(27)/(10)`

Answer 1

Correct Answer - 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.