The set of all points that are at a distance of at least $2$ units from $(-3, 0)$ is

If $t \in R - \{-1\}$,then the locus of the point $\left(\frac{3at}{1+t^3}, \frac{3at^2}{1+t^3}\right)$ is

From a point $P$ on the circle $x^2+y^2=4$,two tangents are drawn to the circle $x^2+y^2-6x-6y+14=0$. If $A$ and $B$ are the points of contact of those lines,then the locus of the centre of the circle passing through the points $P, A$ and $B$ is

If a circle passes through the point $(1, 2)$ and cuts the circle $x^2 + y^2 = 4$ orthogonally,then the equation of the locus of its centre is

The angle between a pair of tangents drawn from a point $P$ to the circle ${x^2} + {y^2} + 4x - 6y + 9{\sin ^2}\alpha + 13{\cos ^2}\alpha = 0$ is $2\alpha$. The equation of the locus of the point $P$ is

If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of a point $S$ satisfying the relation $SQ^2 + SR^2 = 2SP^2$ is