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

$A$ variable circle passes through the fixed point $(2,0)$ and touches the $y$-axis. Then the locus of its centre is

If one end of the diameter is $(1, 1)$ and the other end lies on the line $x+y=3$,then the locus of the centre of the circle is

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

$A$ 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

The equation $\sqrt{(x - 2)^2 + y^2} + \sqrt{(x + 2)^2 + y^2} = 4$ represents a