Let $A(\alpha, 4,7)$ and $B(3, \beta, 8)$ be two points in space. If $Y Z$ plane and $Z X$-plane respectively divide the line segment joining the points $A$ and $B$ in the ratio $2: 3$ and $4: 5$, then the point $C$ which divides $A B$ in the ratio $\alpha: \beta$ externally is

The direction ratios of the line bisecting the angle between the $X$-axis and the line having direction ratios $(3,-1,5)$ are

If the plane $-4 x-2 y+2 z+\alpha=0$ is at a distance of two units from the plane $2 x+y-z+1=0$, then the product of all the possible values of $\alpha$ is

The equation of the locus of a point whose distance from $X Y$-plane is twice its distance from $Z$-axis is