Consider a branch of the hypebola $x^{2} - 2 y^{2} - 22 x - 42 y - 6 = 0$ 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) $1 - \frac{2}{3}$ (B) $\frac{3}{2} - 1$ (C) $1 + \frac{2}{3}$ (D) $\frac{3}{2} + 1$

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Consider a branch of the hypebola

x^{2} - 2 y^{2} - 22 x - 42 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 - \frac{2}{3}

(B)

\frac{3}{2} - 1

(C)

1 + \frac{2}{3}

(D)

\frac{3}{2} + 1

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Question Text

Consider a branch of the hypebola

x^{2} - 2 y^{2} - 22 x - 42 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 - \frac{2}{3}

(B)

\frac{3}{2} - 1

(C)

1 + \frac{2}{3}

(D)

\frac{3}{2} + 1

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