The two points $A$ and $B$ in a plane are such that for all points $P$ lying on a circle satisfying $\frac{PA}{PB} = k$,then $k$ will not be equal to:

If the tangents drawn from a point $P$ to the circle $x^2 + y^2 = a^2$ are perpendicular to the tangents drawn to the circle $x^2 + y^2 = b^2$,then the locus of $P$ is:

If the points $A(2,3)$ and $B(3,2)$ form a triangle with a variable point $P(t, t^2)$,where $t$ is a parameter,then the equation of the locus of the centroid of triangle $ABP$ is:

$A$ variable chord is drawn through the origin to the circle $x^2 + y^2 - 2ax = 0$. The locus of the centre of the circle drawn on this chord as diameter is:

The locus of the center of a variable circle which always touches two given circles externally is

If a tangent to the circle $x^2 + y^2 = 1$ intersects the coordinate axes at distinct points $P$ and $Q,$ then the locus of the mid-point of $PQ$ is