If a bar of given length moves with its extremities on two fixed straight lines at right angles,then the locus of any point marked on the bar describes a/an

The locus of the mid-points of the chords of the circle $x^2 + y^2 - 2x - 4y - 11 = 0$ which subtend $60^o$ at the centre is

The circle passing through the distinct points $(1, t)$,$(t, 1)$,and $(t, t)$ for all values of $t$ passes through the point:

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

Let $x$ and $y$ be real numbers satisfying the equation $x^2 - 4x + y^2 + 3 = 0$. If the maximum and minimum values of $x^2 + y^2$ are $M$ and $m$ respectively,then the numerical value of $M - m$ is:

The locus of a point,which moves such that the sum of squares of its distances from the points $(0,0), (1,0), (0,1), (1,1)$ is $18$ units,is a circle of diameter $d$. Then $d^{2}$ is equal to ...... .