From the origin,chords are drawn to the circle $(x - 1)^2 + y^2 = 1$. The equation of the locus of the midpoints of these chords is

If the locus of the mid-point of the line segment from the point $(3, 2)$ to a point on the circle $x^{2} + y^{2} = 1$ is a circle of radius $r$,then $r$ is equal to:

Let a circle of radius $4$ pass through the origin $O$,the points $A(-\sqrt{3}a, 0)$ and $B(0, -\sqrt{2}b)$,where $a$ and $b$ are real parameters and $ab \neq 0$. Then the locus of the centroid of $\Delta OAB$ is a circle of radius

The locus of the mid-points of chords of the circle $x^{2}+y^{2}=1$,which subtend a right angle at the origin,is

The set of all real values of $\lambda$ for which the point $P$ with coordinates $(\lambda, \lambda^2)$ does not lie inside the triangle formed by the lines $x - y = 0$, $x + y - 2 = 0$, and $x + 3 = 0$ is:

The locus of the midpoints of the chords of the circle $x^{2}+y^{2}=4$ which subtend a right angle at the origin is