Question

Consider an ellipse whose center is at the origin and it's major axis is along the x axis if it's eccentricities is 3/5 and the distance between it's foci is 6then the area of the quadrilateral inscribed in the ellipse with the vertices as the vertices of the ellipse is

Answer 1

Answer:

40 square units

Step-by-step explanation:

Concept:

The required area is in the shape of kite

Area of a kite

=1/2(product of its diagonals)

Given:

Eccentricity e=3/5

Distance between foci= 6

That is

2ae=6

ae=3

a(3/5)=3

a=5

Now,

$b^2=a^2-(ae)^2\\b^2=5^2-3^2\\b^2=25-9\\b^2=16$

b=4

Length of major axis, AA'=2a=10

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