Solve this

​Q1. Consider a branch of the hyperbola 
                   x² – 2y² – $2\sqrt{2x}$ – $4\sqrt{2} y$ – 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 $∆$ ABC is 

      (a) 1 – $\sqrt{2/3}$ sq unit                                (b) $\sqrt{3/2}$ – 1 sq unit

      (c) 1 + $\sqrt{2/3}$ sq unit                                (d) $\sqrt{3/2}$ + 1 sq unit