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Consider a branch of the hypebola `x^2-2y^2-2sqrt2x-4sqrt2y-6=0` with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) `1-sqrt(2/3)` (B) `sqrt(3/2) -1` (C) `1+sqrt(2/3)` (D) `sqrt(3/2)+1`

A

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

B

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

C

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

D

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

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