consider an ellipse whose centre is at the origin and it's major axis is along the x axis. if it's eccentricity is 3/5 and the distance between it's foci is 6 , then the area of the quadrilateral inscribed in the ellipse is
Answer (1)
Student Expert
17th Nov, 2019
Hello there!
Greetings!
We know that ,Area of the quadrilateral inscribed in the ellipse i.e. kite
=1/2(product of its diagonals)
Now it is given, eccentricity e=3/5
Distance between foci= 6
Then,2ae=6
Or,ae=3
a(3/5)=3
Or, a=5
Now, b^2= a^2-(ae)^2
= b^2= 5^2-3^2
Or,b=4
Now, length of major axis, AA'=2a=10
And length of minor axis, BB'=2b=8
Required area
=Area of the kite ABA'B'
=1/2(AA')(BB')
=1/2(10)(8)
=1/2(80)
=40 square units
Thankyou
Greetings!
We know that ,Area of the quadrilateral inscribed in the ellipse i.e. kite
=1/2(product of its diagonals)
Now it is given, eccentricity e=3/5
Distance between foci= 6
Then,2ae=6
Or,ae=3
a(3/5)=3
Or, a=5
Now, b^2= a^2-(ae)^2
= b^2= 5^2-3^2
Or,b=4
Now, length of major axis, AA'=2a=10
And length of minor axis, BB'=2b=8
Required area
=Area of the kite ABA'B'
=1/2(AA')(BB')
=1/2(10)(8)
=1/2(80)
=40 square units
Thankyou
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