Consider a branch of the hyperbola with vertex at the point A

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider a branch of the hyperbola x2−2y2−22x−42y−6=0x^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 (1) 1−231 - \sqrt{\frac{2}{3}} (2) 32−1\sqrt{\frac{3}{2}} - 1 (3) 1+231 + \sqrt{\frac{2}{3}} (4) 32+1\sqrt{\frac{3}{2}} + 1

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