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JEE Advanced2008MathematicsHyperbolaActual

Consider a branch of the hyperbola x^2-2 y^2-2 2 x-4 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 A B C is

Options

  1. A1- 2 3 sq unit
  2. B3 2 -1 sq unit
  3. C1+ 2 3 sq unit
  4. D3 2 +1 sq unit

Correct answer

B. 3 2 -1 sq unit

Step-by-step solution

The given equation can be rewritten as (x- 2 )^2 1 - (y+ 2 )^2 2 =1 for A(x, y) , aligned & e= 1+ 2 4 = 3 2 & x- 2 =2 x=2+ 2 & For C(x, y), x- 2 =a e= 6 & x= 6 + 2 & Now, A C= 6 + 2 -2- 2 = 6 -2 & B C= b^2 a = 2 2 =1 & Area of A B C= 1 2 ( 6 -2) B C & = 1 2 ( 6 -2) 1= 3 2 -1 aligned

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