Question

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

The line $y=x$ and the circle $x^2+y^2-2x=0$ intersect at points $A(0,0),B(1,1)$.
The circle on $AB$ as diameter is
$(x-0)(x-1)+(y-0)(y-1)=0$
or $x^2+y^2-x-y=0$ is the required equation.