The locus of the points from which perpendicular tangents can be drawn to the circle $x^2 + y^2 = a^2$ is

For two points $A(2,1)$ and $B(1,2)$,$P$ is a point such that $PA:PB = 2:1$. Then the locus of $P$ is:

$A$ piece of paper in the shape of a sector of a circle (see $Fig. 1$) is rolled up to form a right-circular cone (see $Fig. 2$). The value of the angle $\theta$ is

The line segment joining the points $(-5, 1)$ and $(3, 2)$ subtends a right angle at a variable point $P$. Find the locus of the point $P$.

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

Let $A = (a, 0)$ and $B = (-a, 0)$ be two fixed points. For $a \in (-\infty, 0)$,point $P(x, y)$ moves in the plane such that $PA = nPB$ $(n \neq 0, n \neq 1)$. If $0 < n < 1$,then which of the following is true regarding the locus of $P$?