Physics-
General
Easy

Question

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

  1. open parentheses fraction numerator 1 over denominator 2 end fraction comma blank minus fraction numerator 1 over denominator 2 end fraction close parentheses  
  2. open parentheses fraction numerator 1 over denominator 2 end fraction comma blank fraction numerator 1 over denominator 3 end fraction close parentheses  
  3. left parenthesis negative 1 comma blank 0 right parenthesis  
  4. open parentheses negative fraction numerator 1 over denominator 2 end fraction comma blank fraction numerator 1 over denominator 2 end fraction close parentheses  

The correct answer is: open parentheses negative fraction numerator 1 over denominator 2 end fraction comma blank fraction numerator 1 over denominator 2 end fraction close parentheses


    The smallest circle means that its radial is, distance from origin to the diameter is smallest.

    Let equation of line perpendicular to y minus x equals 1 is x plus y equals lambda
    Also, it passes through (0, 0)
    therefore blank lambda equals 0
    therefore blankPerpendicular line is x plus y equals 0
    The intersection point of lines are open parentheses negative fraction numerator 1 over denominator 2 end fraction comma fraction numerator 1 over denominator 2 end fraction close parentheses
    Which is the centre of circle.
    Alternate It is clear from the figure that centre lies on IInd quadrant.
    Hence, option (d) is correct

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