If z = x + iy, then on the basis of information given in List-I match the answers in List-II.

	List- I		List- II
(P)	If  $||z+i|-|z-5i||=2a$  represents a hyperbola then number of integral values of ‘a’ are	(1)	1
(Q)	Area enclosed by the rays with equations $\arg (z+1)=\pm \frac{\pi }{4}$  and  $\text{arg}(\text{z}-\text{1})=\pm \frac{3\pi }{4}$ is ___sq. units	(2)	2
(R)	If $f\left(z\right)=(2z-3)i$, where  $f\left(z\right)$ is always real and $-5\le f\left(z\right)\le 5,$then number of common solution(s) of  $f\left(z\right)\text{ and }|\text{z}-\frac{\text{5}}{\text{2}}|=1$ is/are	(3)	3
(S)	If roots of  ${(z-5)}^6=64$  represents a regular hexagon and distance between its two parallel sides is  $\lambda$, then the value of  $\frac{{\lambda }^2}{2}$ is	(4)	6