Question

The locus of the middle point of the chord of the circle $x^2+y^2-2x=0$ passing through the origin is

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

Answer 1

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

$x^2+y^2-2x=0$
Centre $=(2,0)$, radius $=1$
Let AB is a chord Passing through origin.
Equation of AB is $y=mx$
$\therefore x^2+y^2-2x=0$
$x^2+m^2{x}^2-2x=0$
$x=0$ and $x=\frac{2}{1+m^2}$
& $y=0$ and $y=\frac{2m}{1+m^2}$
So, mid point of chord is $x=\frac{1}{1+m^2}$ & $y=\frac{m}{1+m^2}$
$x^2+y^2=\frac{1}{1+m^2}=x$
$\Rightarrow x^2+y^2-x=0$