JEE MAIN - Mathematics (2017 - 8th April Morning Slot - No. 9)
Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is $${3 \over 5}$$ and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
8
32
80
40
Explanation
e = 3/5 & 2ae = 6 $$ \Rightarrow $$ a = 5
$$ \because $$ b2 = a2 (1 $$-$$ e2)
$$ \Rightarrow $$ b2 = 25(1 $$-$$ 9/25)
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$$ \Rightarrow $$ b = 4
$$ \therefore $$ Area of required quadrilateral
= 4(1/2 ab) = 2ab = 40
$$ \because $$ b2 = a2 (1 $$-$$ e2)
$$ \Rightarrow $$ b2 = 25(1 $$-$$ 9/25)
$$ \Rightarrow $$ b = 4
$$ \therefore $$ Area of required quadrilateral
= 4(1/2 ab) = 2ab = 40
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