An ellipse passing through `(4sqrt2,2sqrt6)` has foi at `(-4,0) and (4, 0)`. Then, its eccentricity is

Options

A. `sqrt(2)`
B. `(1)/(2)`
C. `(1)/(sqrt(2))`
D. `(1)/(sqrt(3))`

Answer

B

Explanation

The y-coordinate of foci is zero.
`therefore `Major axis is on X-axis
i.e., ae=4.
let equation of ellipse be
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`therefore((4sqrt(2))^(2))/(a^(2))+((2sqrt(6))^(2))/(a^(2)-16)=1`
`[becauseb^(2)=a^(2)(1-e^(2))=a^(2)-16]`
`implies(32)/(a^(2))+(24)/(a^(2)-16)=1`
`implies32a^(2)-512+24a^(2)=a^(2)(a^(2)-16)`
`implies56a^(2)-512=a^(4)-16a^(2)`
`impliesa^(4)-72a^(2)+512=0`
`a^(4)-64a^(2)-8a^(2)+512=0`
`impliesa^(2)(a^(2)-64)-8(a^(2)-64)=0`
`implies(a^(2)-8)(a^(2)-64)=0`
`impliesa^(2)=64`
`impliesa=8`
`[because=-8" in not possible"]`
`becauseae=4`
`implies8xxe=4`
`therefore e=1//2`