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Consider an ellipse, whose centre is at the origin and its major axis is along the
x-axis.  If its eccentricity is \small \frac{3}{5}  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

 

Answers (2)

best_answer

As we learnt in 

Length of major axis -

2a

- wherein

a\rightarrow Semi major axis

 

 

Length of major axis -

2b

- wherein

b\rightarrow Semi minor axis

 

 

Eccentricity -

e= \sqrt{1-\frac{b^{2}}{a^{2}}}

- wherein

For the ellipse  

\frac{x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}= 1

 e=\frac{3}{5}

2ae=6\; \Rightarrow ae=3

Hence a=5

b^{2}=a^{2}(1-e^{2})=>b=4

Area of quadrilateral ABCD = 4 ar \Delta AOB

=4\times \frac{1}{2}\times a\times b

=4\times \frac{1}{2}\times 5\times 4

=4 \times 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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Aadil

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