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KCET2009MathematicsCircle

The coordinates of the centre of the smallest circle passing through the origin and having y = x +1 as a diameter are

Options

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

Correct answer

D. (- 1 2 , 1 2 )

Step-by-step solution

The smallest circle means that its radial is, distance from origin to the diameter is smallest. Let equation of line perpendicular to y-x=1 is x + y = . Also, it passes through (0,0) . =0 Perpendicular line is x + y =0 . The intersection point of lines are (- 1 2 , 1 2 ) . Which is the centre of circle.

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