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A vertex of a branch of the hyperbola x^...

A vertex of a branch of the hyperbola `x^(2)-2y^(2)-2sqrt(2)x-4sqrt(2)y-6=0`, `B` is one of the end points of its latuscrectum and `C` is the focus of the hyperbola nearest to the point `A`.
Statement-`1` : The area of `DeltaABC` is `((sqrt(3))/(2)-1)` sq. units.
Statement-`2` : Eccentricity of the hyperbola is `(sqrt(3))/(2)` and length of the conjugate axis is `2sqrt(2)`.

A

`1-sqrt((2)/(3))`

B

`sqrt((3)/(2))-1`

C

`1+sqrt((2)/(3))`

D

`sqrt((3)/(2))+1`

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