The locus of a point which moves so that its distance from the $x$-axis is double its distance from the $y$-axis is:

If $A(2, 3)$ and $B(2, -3)$ are two points,then the equation of the locus of a point $P$ such that $PA + PB = 8$ is

The locus of the middle points of chords of the circle $x^2 + y^2 - 2x - 6y - 10 = 0$ which pass through the origin is:

If 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 $2 \alpha$,then the equation of the locus of $P$ is

The locus of the centre of the circle touching the $x$-axis and passing through the point $(-1, 1)$ is

The locus of the midpoints of the chords of the circle $x^2+y^2=16$,which are tangents to the hyperbola $9x^2-16y^2=144$,is