If a circle is inscribed in an equilateral triangle of side $a$, then the area of any square (in sq units) inscribed in this circle 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

If power of a point $(4,2)$ with respect to the circle $x^2+y^2-2 \alpha x+6 y+\alpha^2-16=0$ is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is