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JEE Main2009MathematicsStraight LinesActual

Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1,0) to the distance from the point (-1,0) is equal to 1 3 . Then the circumcentre of the triangle A B C is at the point

Options

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

Correct answer

B. ( 5 4 , 0 )

Step-by-step solution

aligned & P=(1,0) ; Q(-1,0) & Let A=(x, y) & A P A Q = B P B Q = C P C Q = 1 3 & 3 A P=A Q 9 A P^2=A Q^2 9(x-1)^2+9 y^2=(x+1)^2+y^2 & 9 x^2-18 x+9+9 y^2=x^2+2 x+1+y^2 8 x^2-20 x+8 y^2+8=0 & x^2+y^2- 5 2 x+1=0 aligned A lies on the circle Similarly B, C are also lies on the same circle Circumcentre of ABC = Centre of Circle (1)= ( 5 4 , 0 )

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