Question

The locus of the mid points of the chords of the circle $x^2-2 x+y^2=0$ drawn from a point $(0,0)$ on it is

• A. $x^2+y^2-x=0$
• B. $2 x^2+y^2-2=0$
• C. $y^2+x-1=0$
• D. $y+x^2+2 x-3=0$

Answer 1

Answer: (A)

Given circle, $x^2-2 x+y^2=0$
Centre $C(1,0)$
The locus of the mid-points of the chords of given circle from point $(0,0)$ is a circle whose extremities of diameter is centre and given point.
Locus of mid-points of the chord is
$ (x-1)(x-0)+(y-0)(y-0)=0 $
$ \Rightarrow x^2-x+y^2=0$
or $x^2+y^2-x=0$