The locus of the centre of a circle,which touches two given circles externally,is

If $A=(1,2)$,$B=(2,1)$ and $P$ is any point satisfying the condition $PA+PB=3$,then the equation of the locus of $P$ is

The locus of the centre of a circle touching both the coordinate axes is

$A$ bottle in the shape of a right-circular cone with height $h$ contains some water. When its base is placed on a flat surface,the height of the vertex from the water level is $a$ units. When it is kept upside down,the height of the base from the water level is $\frac{a}{4}$ units. Then the ratio $\frac{h}{a}$ is

$A$ line through $(0,0)$ cuts the circle $x^2 + y^2 - 2ax = 0$ at points $A$ and $B$. The locus of the centre of the circle drawn on $AB$ as a diameter 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