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

$A$ point $P(x, y)$ divides the line segment joining the points $(5, 0)$ and $(10 \cos \theta, 10 \sin \theta)$ in the ratio $2 : 3$. Find the locus of point $P$ as $\theta$ varies.

Let $P(\alpha, \beta)$ be a variable point which moves in the $x-y$ plane such that $\frac{PA}{PB} = 2$,where $A(1, 0)$ and $B(0, -1)$. If $M$ and $m$ denote respectively the maximum and minimum value of $\alpha + \beta$,then the value of $[\frac{M}{m}]$ is- (where $[.]$ denotes the greatest integer function)

$A$ point $P(x, y)$ is such that the sum of squares of its distances from the coordinate axes is equal to the square of its distance from the line $x-y=1$. Then the equation of the locus of $P$ is

The locus of a point which moves such that the sum of the squares of its distances from the sides of a square of side length $1$ is $9$,is

The locus of a point,such that the difference of the squares of the lengths of the tangents drawn from it to two given circles is constant,is: