Let $(x, y)$ be such that $\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2}$. Match the statements in Column $I$ with the statements in Column $II$.

Column $I$	Column $II$
$(A)$ If $a=1$ and $b=0$,then $(x, y)$	$(p)$ lies on the circle $x^2+y^2=1$
$(B)$ If $a=1$ and $b=1$,then $(x, y)$	$(q)$ lies on $(x^2-1)(y^2-1)=0$
$(C)$ If $a=1$ and $b=2$,then $(x, y)$	$(r)$ lies on $y=x$
$(D)$ If $a=2$ and $b=2$,then $(x, y)$	$(s)$ lies on $(4x^2-1)(y^2-1)=0$

• A
  $A \rightarrow p; B \rightarrow q; C \rightarrow p; D \rightarrow s$
• B
  $A \rightarrow q; B \rightarrow s; C \rightarrow s; D \rightarrow q$
• C
  $A \rightarrow q; B \rightarrow r; C \rightarrow p; D \rightarrow r$
• D
  $A \rightarrow r; B \rightarrow s; C \rightarrow q; D \rightarrow p$