The equation of the circle which passes through $(1, 0)$ and $(0, 1)$ and has its radius as small as possible,is

$A$ circle passing through the point $P(\alpha, \beta)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$. The point $P$ is above the line $AB$. The point $Q$ on the line segment $AB$ is the foot of the perpendicular from $P$ on $AB$. If $PQ$ is equal to $11$ units,then the value of $\alpha \beta$ is $.............$.

The position of the point $(0.1, 3.1)$ with respect to the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ is:

If one end of the diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$,then the other end of the diameter is

$A$ circle touches both the coordinate axes and the straight line $L \equiv 4x+3y-6=0$ in the first quadrant. If this circle lies below the line $L=0$,then the equation of that circle is

If one end of a diameter of the circle $3x^{2}+3y^{2}-9x+6y+5=0$ is $(1,2)$, then the other end is