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 a diameter is ............

• A. $x^2+y^2+x+y=0$
• B. $x^2+y^2-x-y=0$
• C. $x^2+y^2-3x+y=0$
• D. $x^2+y^2+3x-y=0$

Answer 1

Answer: (B)

We have equation of line $y=x$ and equation of circle $x^2+y^2-2x=0$

Now, intersecting points of given line and circle,
$x^2+x^2-2x=0$
$\Rightarrow 2x^2-2x=0$
$\Rightarrow 2x(x-1)=0$
$\Rightarrow x=0,1$
when $x=0$ then $y=0$ and when $x=1$ then $y=1$
$\therefore$ Coordinates of end points of diameter $AB$ are (0,0) and (1,1)
$\therefore$ Required equation of circle with diameter $AB$
$(x-0)(x-1)+(y-0)(y-1)=0$
$\Rightarrow x^2-2+y^2-y=0$
$\Rightarrow x^2+y^2-x-y=0$