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

Let a point $P$ be such that its distance from the point $(5, 0)$ is thrice the distance of $P$ from the point $(-5, 0)$. If the locus of the point $P$ is a circle of radius $r$,then $4r^{2}$ is equal to ...... .

$A$ circle touches the $X$-axis and also touches the circle with radius $2$ and center at $(0, 3)$. Find the locus of the center of the circle.

If a circle passing through $A(1,1)$ touches the $X$-axis,then the locus of the other end of the diameter through $A$ is

The coordinates of the points $A$ and $B$ are $(ak, 0)$ and $(\frac{a}{k}, 0)$,where $k = \pm 1$. If a point $P(x, y)$ moves such that $PA = kPB$,then the equation to the locus of $P$ is:

If $P(1, 0)$,$Q(-1, 0)$,and $R(2, 0)$ are three given points,then find the locus of $S(x, y)$ which satisfies the relation $SQ^2 + SR^2 = 2SP^2$.