The line $4 x+3 y-4=0$ divides the circumference of a circle in the ratio $1: 2$. If $C(5,3)$ is the centre of that circle, then equation of the circle is

Two sides of a square are along the lines $x=-5$ and $y=4$. The point of intersection of the diagonals is $(3,-4)$. The point of intersection of the tangents drawn to the circumcircle of the square at the two consecutive vertices lying on $x=-5$ is

If $L_1, L_2$ and $L_3$ are the chords of contact of the three points $(2,0),(1,-2)$ and $(4,4)$ respectively with respect to the circle $x^2+y^2=3$, then $L_1, L_2$ and $L_3$ are

The combined equation of the direct common tangents of the circles $x^2+y^2+2 x=0$ and $x^2+y^2-2 y-3=0$