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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Mathematics
Chapter
Ellipse

JEE Main 2017 · 8 April · Online · Mathematics · Ellipse

Consider an ellipse, whose center is at the origin and its major...

Consider an ellipse, whose center is at the origin and its major axis is along the xx-axis. If its eccentricity is 35\dfrac{3}{5} and the distance between its foci is 66, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:Consider an ellipse, whose center is at the origin and its major axis is along the x -axis. If its eccentricity is

Options

  1. A3232
  2. B8080
  3. C4040
  4. D88

Correct answer

C. 4040

Step-by-step solution

Consider an ellipse, whose center is at the origin and its major axis is along the x -axis. If its eccentricity is

Given eccentricity of the ellipse e=35.e = \dfrac{3}{5} .

Distance between foci is 2ae=62ae = 6
→a=5.\to a = 5.

Also, b2=a2(1−e2){b}^{2} = {a}^{2} ( 1 − {e}^{2} )

→\to b2=25(1−925){b}^{2} = 25\left(1 - \dfrac{9}{25}\right)

→\to b=4b = 4

Area =4(12ab)=2ab=40= 4\left(\dfrac{1}{2}ab\right) = 2ab = 40
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