Let $\pi$ be the plane parallel to y-axis and containing the points (1, 0, 1) and (3, 2,  1). Also $A\equiv (4,0,0)$ and $B\equiv (6,0,-2)$ are two points and $P(x_0,y_0,z_0)$ is a variable point on the plane $\pi =0,$ which of the following statement(s) is(are) CORRECT.

Let the plane be $\alpha x+\beta z+1=0$  
Passes through (1, 0, 1) & (3, 2 –1) 
$\therefore \alpha =-\frac{1}{2},\beta =-\frac{1}{2}$ 
$\therefore \left(P\right)x+z=2$ 
(Q) Both A & B are same side of P reflection of A in plane is A’(2, 0, –2) equation of line
$A\text{'}B:\overline{r}=6\widehat{i}-2\widehat{k}+\lambda \left(4\widehat{i}\right)$ for $P:6+4\lambda +0-2=Z\Rightarrow \lambda ={\gamma }_2$  
(R) ${|PA-PB|}_{\min }=0\Rightarrow {|PA-PB|}_{\min }$ will approach AB
$AB=\sqrt{4+0+4}=\sqrt{8}$ 
$|PA-PB|\in [0,\sqrt{8})$ 
(S) Also, A’ will lie on $\frac{x-2}{1}=\frac{y-\alpha }{0}=\frac{z+B}{-1}$ 
$\Rightarrow \frac{2-2}{1}=\frac{0-\alpha }{0}=\frac{-2+\beta }{-1}$ 
$\Rightarrow \alpha =0,\beta =2$ 
${\alpha }^4+{\beta }^4=16$