#### The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse Option 1) Option 2) 18 Option 3) Option 4) 27

As we have discussed in

Length of latus rectum of ellipse -

- wherein

For the ellipse

Coordinates of foci -

- wherein

For the ellipse

Eccentricity -

- wherein

For the ellipse

Equation of tangent is

a2 = 9, b2 = 5

Hence, endpoints of LRs =

Thus, equation of one of tangent is

If y = 0

If x = 0

Hence, area of

Option 1)

This option is incorrect.

Option 2)

18

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

27

This option is correct.