From the origin, chords are drawn to the circle (x - 1)2 + y2 = 1, then equation of locus of middle points of these chords, is -

Question

From the origin, chords are drawn to the circle (x - 1)2 + y2 = 1, then equation of locus of middle points of these chords, is - (A) x2 + y2 = 1 (B) x2 + y2 = x (C) x2 + y2 = y (D) None of these

Tardigrade Admin · Accepted Answer

Here equation of the given circle is x2 + y2 - 2x = 0 This clearly passes through origin Hence if (x1, y1) be midpoint of the chord then its equation is given by T = S1 ⇒ xx1 + yy1 - (x + x1) = x12 + y12 - 2x1 or xx1 + yy1 - x = x12 + y12 - x1 This passes through the origin (0, 0) ∴ x12 + y12 - x1 = 0 ∴ Required locus is x2 + y2 = x

Q. From the origin, chords are drawn to the circle $(x - 1)^{2} + y^{2} = 1$ , then equation of locus of middle points of these chords, is -

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

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

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

None of these

Q. From the origin, chords are drawn to the circle (x−1)2+y2=1, then equation of locus of middle points of these chords, is -

x2+y2=1

x2+y2=x

x2+y2=y

None of these

Q. From the origin, chords are drawn to the circle $(x - 1)^{2} + y^{2} = 1$ , then equation of locus of middle points of these chords, is -

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

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

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