If the equation of a curve remains unchanged by replacing $x$ with $y$ and $y$ with $x$,then the curve is

Ten ants are on the real line. At time $t=0$,the $k$-th ant starts at the point $k^2$ and,travelling at a uniform speed,reaches the point $(11-k)^2$ at time $t=1$. The number of distinct times at which at least two ants are at the same location is

If the line segment joining the points $(1,0)$ and $(0,1)$ subtends an angle of $45^{\circ}$ at a variable point $P$,then the equation of the locus of $P$ is

$A$ straight line passes through a fixed point $(h, k)$. The locus of the foot of the perpendicular drawn from the origin to this line is:

The locus of the point $P(x, y)$ such that the area of the $\triangle PAB$ is $7$,where $A(4, 5)$ and $B(-2, 3)$ are given points,is

If $P(x, y)$ is a variable point which is at a distance of $2$ units from the line $2x - 3y + 1 = 0$ and $\sqrt{13}$ units from the point $(5, 6)$,then the equation of the locus of $P$ is: