Mathematics

Problem

Consider a branch of the hyperbola

x^2 - 2y^2 - 2\sqrt{2}x - 4\sqrt{2}y - 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{\frac{2}{3}}

\sqrt{\frac{3}{2}} - 1

1 + \sqrt{\frac{2}{3}}

\sqrt{\frac{3}{2}} + 1

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