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)

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

Answer 2

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