Question

The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB$. Equation of the circle with $AB$ as diameter is

• A. $x^2+y^2=1$
• B. $x(x-1)+y(y-1)=0$
• C. $x^2+y^2=2$
• D. $(x-1)(x-2)+(y-1)(y-2)=0$

Answer 1

Answer: (B)

$x(x-1)+y(y-1)=0$

The intersection of the line and the circle is
$x^2+x^2-2x=0$
$\Rightarrow$ $2x(x-1)=0$
$\Rightarrow$ $x=0,1$
$\Rightarrow$ $y=0,1$
$\therefore$ The points $(0,0)$ and $(1,1)$ are the end points of a diameter of circle
$\therefore$ Its equation is
$(x-0)(x-1)+(y-0)(y-1)=0$
$\Rightarrow x^2+y^2-x-y=0$