The locus of the mid points of the chords of the circle x2-2 x+y2=0 drawn from a point (0,0) on it is

Question

The locus of the mid points of the chords of the circle x2-2 x+y2=0 drawn from a point (0,0) on it is (A) x2+y2-x=0 (B) 2 x2+y2-2=0 (C) y2+x-1=0 (D) y+x2+2 x-3=0

Tardigrade Admin · Accepted Answer

Given circle, x2-2 x+y2=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 ⇒ x2-x+y2=0 or x2+y2-x=0

Q. 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

$x^{2} + y^{2} - x = 0$

$2 x^{2} + y^{2} - 2 = 0$

$y^{2} + x - 1 = 0$

$y + x^{2} + 2 x - 3 = 0$

Q. The locus of the mid points of the chords of the circle x2−2x+y2=0 drawn from a point (0,0) on it is

x2+y2−x=0

2x2+y2−2=0

y2+x−1=0

y+x2+2x−3=0

Given circle, x2−2x+y2=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 ⇒x2−x+y2=0 or x2+y2−x=0

Q. 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

$x^{2} + y^{2} - x = 0$

$2 x^{2} + y^{2} - 2 = 0$

$y^{2} + x - 1 = 0$

$y + x^{2} + 2 x - 3 = 0$