Statement 1 : If a circle S = 0 intersects a hyperbola xy = 4 at four points. Three of them are (2, 2), (4, 1) and (6, 2/3), then coor- dinates of the fourth point are (1/4, 16)

Statement 2 : If a circle S = 0 intersects a hyperbola $\mathrm{xy}= {\mathrm{c}}^2 \mathrm{at} {\mathrm{t}}_1 , {\mathrm{t}}_2 , {\mathrm{t}}_3 , {\mathrm{t}}_4 \mathrm{then} {\mathrm{t}}_1 {\mathrm{t}}_2 {\mathrm{t}}_3 {\mathrm{t}}_4 =1$
Then correct statement is

$$\begin{gathered} \mathrm{Given} \mathrm{hyperbola} \mathrm{xy}=c^2 \\ \mathrm{let} \left(\mathrm{c} \mathrm{t}, \frac{\mathrm{c}}{\mathrm{t}}\right) \mathrm{be} \mathrm{any} \mathrm{point} \mathrm{on} \mathrm{given} \mathrm{hyperbola}. \\ \underline{\mathrm{Statement}-\mathrm{I}} : \mathrm{xy}=4 \\ \Rightarrow c^2=4 \\ \Rightarrow c=2 \\ \Rightarrow {\mathrm{t}}_1(2, 2), {\mathrm{t}}_2(4, 1) {\mathrm{t}}_3(6, \frac{2}{3}) \mathrm{are} \mathrm{given} \mathrm{three} \mathrm{points} \\ \Rightarrow {\mathrm{t}}_1=1, {\mathrm{t}}_2=2, {\mathrm{t}}_2=3 \\ \mathrm{Now} {\mathrm{t}}_1.{\mathrm{t}}_2.{\mathrm{t}}_3.{\mathrm{t}}_4=1 \Rightarrow 6{\mathrm{t}}_4= \Rightarrow {\mathrm{t}}_4=\frac{1}{6} \\ \mathrm{Now} \mathrm{fourth} \mathrm{point}=\left(c{t}_4, \frac{c}{{\mathrm{t}}_4}\right)=\left(\frac{1}{3}, 12\right) \\ \therefore \mathrm{Statement} \mathrm{I} \mathrm{is} \mathrm{false}. \\ \mathrm{we} \mathrm{know} \mathrm{that} \mathrm{if} \mathrm{a} \mathrm{circle} \mathrm{S}=0 \mathrm{intersects} \mathrm{hyperbola} \\ \mathrm{xy}={\mathrm{c}}^2 \mathrm{at} {\mathrm{t}}_1, {\mathrm{t}}_2, {\mathrm{t}}_3, {\mathrm{t}}_4 \mathrm{then} {\mathrm{t}}_1 {\mathrm{t}}_2 {\mathrm{t}}_3 {\mathrm{t}}_4=1 \\ \therefore \mathrm{Statement} \mathrm{II} \mathrm{is} \mathrm{true} \end{gathered}$$