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Consider a branch of the hypebola x^2-2y...

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`

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B
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