$\text{ If a circles }{x}^2+y^2=a^2\text{ and the }$$\text{ rectangular hyperbola }xy=c^2$$\text{ intersect in four points, }\left(c{t}_r,\frac{c}{t_r}\right)\text{ , }$$r=1,2,3,4\text{ then }{t}_1{t}_2{t}_3{t}_4\text{ is equal to }$

$\begin{array}{l}\text{Parametric equation of the hyperbola }xy=c^2\text{\hspace{0.33em} is }\left(ct,\frac{c}{t}\right)\\ \text{substitute this point in the circle }{x}^2+y^2=a^2\\ c^2{t}^4-a^2{t}^2+c^2=0 for which t_1,t_2,t_3,t_4 are roots\\ \text{Hence, }{t}_1{t}_2{t}_3{t}_4=product of roots=\frac{c^2}{c^2}=1\end{array}$