The locus of the point which is equidistant from the point $(1,1)$ and the line $x+y+1=0$ is

$A$ stick of length $l$ rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is

Let $C$ be the centre and $A$ be one end of a diameter of the circle $x^2+y^2-2x-4y-20=0$. If $P$ is a point such that $A$ divides $CP$ in the ratio $2:3$,then the locus of $P$ is

Let $S$ be the set of points on the $X$-axis lying at a distance of $d$ units from $(3, 4)$. Which of the following is true?

For a real variable $a > 1$,consider the points $A_k = (k a, a^k)$,$k = 1, 2, \ldots, n$ in the Cartesian plane. If $\alpha$ and $\beta$ represent respectively the arithmetic mean of $x$-coordinates and the geometric mean of $y$-coordinates of $A_k$,then the locus of the point $P(\alpha, \beta)$ is

The locus of the midpoint of a chord of the circle $x^{2} + y^{2} = 4$ which subtends an angle of $45^{\circ}$ at the major arc of the circle is: