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KVPY2013MathematicsParabola

The vertices of the base of an isosceles triangle lie on a parabola y²=4 x and the base is a part of the line y=2 x-4 . If the third vertex of the triangle lies on the x -axis, its coordinates are

Options

  1. A( 5 2 , 0 )
  2. B( 7 2 , 0 )
  3. C( 9 2 , 0 )
  4. D( 11 2 , 0 )

Correct answer

C. ( 9 2 , 0 )

Step-by-step solution

array l (2 x-4)²=4 x (x-2)²=x x²-5 x+4=0 x=1,4 array array l C (1,-2) B (4,4) AB = AC ( -4)²+16 = ( -1)²+4 array On solving, we get = 9 2

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