4.1 complex nubers — MATHS STD 11 Science — Question

$S=\left\{X \in R ^3:(\operatorname{dist}(X, P))^2-(\operatorname{dist}(X, Q))^2=50\right\} \text { and }$

$T=\left\{Y \in R ^3:(\operatorname{dist}(Y, Q))^2-(\operatorname{dist}(Y, P))^2=50\right\}.$

Then which of the following statements is (are) $TRUE$?

$(A)$ There is a triangle whose area is $1$ and all of whose vertices are from $S$.

$(B)$ There are two distinct points $L$ and $M$ in $T$ such that each point on the line segment $L M$ is also in $T$.

$(C)$ There are infinitely many rectangles of perimeter $48$ , two of whose vertices are from $S$ and the other two vertices are from $I$.

$(D)$ There is a square of perimeter $48$ , two of whose vertices are from $S$ and the other two vertices are from $T$.