# Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis.  If its eccentricity is   and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is : Option 1) 8 Option 2) 32 Option 3) 80 Option 4) 40

As we learnt in

Length of major axis -

- wherein

Semi major axis

Length of major axis -

- wherein

Semi minor axis

Eccentricity -

- wherein

For the ellipse

Hence a=5

Area of quadrilateral ABCD = 4 ar

=4  10 = 40

Option 1)

8

This option is incorrect

Option 2)

32

This option is incorrect

Option 3)

80

This option is incorrect

Option 4)

40

This option is correct

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