- A$\text{A}\subset\text{B}$
- ✓$\text{B}\subset\text{A}$
- C$\text{A}=\phi$
- D$\text{B}=\phi.$
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$S=\left\{X \in R ^3:(\operatorname{dist}(X, P))^2-(\operatorname{dist}(X, Q))^2=50\right\} \text { and }$
$T=\left\{Y \in R ^3:(\operatorname{dist}(Y, Q))^2-(\operatorname{dist}(Y, P))^2=50\right\}.$
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 $T$.
$(A)$ $\frac{\pi}{2}$ $(B)$ $\frac{\pi}{6}$ $(C)$ $\frac{2 \pi}{3}$ $(D)$ $\frac{5 \pi}{6}$