The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is

If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same line that are 5 units away from $A$ are

If each of the points $(a, 4),(-2, b)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $(a, b)$ lies on the line

$A(-4,0)$ and $B(4,0)$ are two fixed points. $C$ and $D$ are two points on $Y$ - axis such that $C D=4$ and $C$ is a point below $D$. Then, the locus of the point of intersection of the lines $A C$ and $B D$ is