Question

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

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

Answer 1

The correct option is A $x^2+y^2-x-y=0$

The equation of line is $y=x$ ...(1)
and equation of circle is $x^2+y^2-2x=0$ ...(2)
On solving (1) and (2), we get
$x^2+x^2-2x=0\Rightarrow 2x^2-2x=0\Rightarrow 2x(x-1)=0\Rightarrow x=0,x=1$
When $x=0,y=0$ and $x=1,y=1$
Let coordinate of $A$ is $(0,0)$ and co-ordinate of $B$ is $(1,1)$
Therefore equation of circle is
$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0\Rightarrow (x-0)(x-1)+(y-0)(y-1)=0\Rightarrow x^2-x+y^2-y=0$

$\Rightarrow x^2+y^2-x-y=0$