Find the length of latus rectum L of ellipse `(x^(2))/(A^(2)) + (y^(2))/(9) = 1, (A^2) gt 9)` where`A^2` is the area enclosed by quadrilateral formed by joining the focii of hyperbola `(x^(2))/(16) - (y^(2))/(9) = 1` and its conjugate hyperbola

Options

A. `(18sqrt(2))/(5)`
B. `(5)/(18)sqrt(2)`
C. `(18)/(5sqrt(2))`
D. `(9)/(5sqrt(2))`

Answer

C

Explanation

Area of quadrilateral by joining focii of hyperbola and its conjugate hyperbola is `2(ae)^(2)` i.e., `2(5^(2)) = 50`
`therefore " " i.e., A^(2) = 50 rArr A =5 sqrt(2)`
Now length of laths rectum `= ((2b^(2))/(a))`
` =(2.9)/(5 sqrt(2)) = (18)/(5sqrt(2))`