JEE Main Math Class 11 Coordinate Geometry Part 1 Questions

The end point of latus rectum of ellipse
‌

x2

a2

+‌

y2

b2

=1 in first quadrant is (ae,‌

b2

a

) and the tangent at this point intersects x -axis at (‌

a

e

,0) and y -axis at (0,a).
The given ellipseis ‌

x2

9

+‌

y2

5

=1
Then a2=9,b2=5
⇒e=√1−‌

5

9

=‌

2

3

∴ End point of latus rectum in first quadrant is L(2,5∕3)
Equation of tangent at L is ‌

2x

9

+‌

y

3

=1
[∵ It meets x -axis at A(9∕2,0) and y -axis at B(0,3)]
Area of ∆OAB=‌

1

2

×‌

9

2

×3=‌

27

4

By symmetry area of quadrilateral
=4×( Area ∆OAB)=4×‌

27

4

=27 sq. units