Q127 / 225 · JEE Main 2004 · 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 on $\mathrm{AB}$ as a diameter is

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

Solution

Points of intersection of line $y=x$ with $x^2+y^2-2 x=0$ are $(0,0)$ and $(1,1)$ hence equation of circle having end points of diameter $(0,0)$ and $(1,1)$ is $x^2+y^2-x-y=0$

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

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