Q49 / 160 · WBJEE 2011 · Mathematics

The intercept on the line \(y=x\) by the circle \(x^2+y^2-2 x=0\) is \(A B\). Equation of the circle with \(A B\) as diameter is

  • A
    \(x^2+y^2=1\)
  • Correct answer
    B
    \(\mathrm{x}(\mathrm{x}-1)+\mathrm{y}(\mathrm{y}-1)=0\)
  • C
    \(x^2+y^2=2\)
  • D
    \((x-1)(x-2)+(y-1)+(y-2)=0\)

Solution

Hints: \(2 x^2-2 x=0 \quad x(x+1)=0 \quad x=0,1 ; y=0,1\) \((0,0),(1,1)\) as diametric ends \(\begin{aligned} & (x-0)(x-1)+(y+0)(y-1)=0 \\ & x^2+y^2-x-y=0 \end{aligned}\)

Hence, the correct answer is option: 'B'.

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