Correct Answer - A
As eccentricity of ellipse `= (4)/(3)`
Coordinate of foci `= (4,0), (-4,0)`
`rArr (4,-(9)/(5))` is one of the end point of latus-rectum
`rArr` Required area is
`(1)/(2pi) xx pi xx (4^(2) + (9^(2))/(5^(2))) xx 2 tan^(-1) ((9)/(20)) -` area of `Delta POQ`
`= (481)/(25) tan^(-1) ((9)/(20)) -(1)/(2) xx 4xx ((18)/(5))`
`= (481)/(25) tan^(-1) ((9)/(20)) -(36)/(5)`