At which point on the line $x = 3$ are the tangents drawn to the circle $x^2 + y^2 = 8$ perpendicular to each other?

The locus of the mid-points of the chords of the circle $x^{2}+y^{2}+2x-2y-2=0$ which make an angle of $90^{\circ}$ at the centre is

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

The locus of all points that are at a distance greater than $2$ units from $(-3, 0)$ is:

Let $A = (0, 4)$ and $B = (2 \cos \theta, 2 \sin \theta)$,for some $0 < \theta < \frac{\pi}{2}$. Let $P$ divide the line segment $AB$ in the ratio $2:3$ internally. The locus of $P$ is

The perimeter of the locus of the point $P$ which divides the line segment $QA$ internally in the ratio $1:2$,where $A=(4,4)$ and $Q$ lies on the circle $x^2+y^2=9$ is