JEE Main 2008 Mathematics question on Conic Sections

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 latusrectum. If $C$ is the focus of the hyperbola nearest to the point $A$, then the area of the $\triangle ABC$ is