Statement 1 : There are infinite points from which two mutually perpendicular tangents can be drawn to the hyperbola $\frac{{\mathrm{x}}^2}{9}-\frac{{\mathrm{y}}^2}{16}=1$

Statement 2 : The locus of point of intersection of perpendicular tangents lies on the circle
Then correct statement is

 :$$\begin{gathered} Statement-I:Given hyperbola \frac{x^2}{9}-\frac{y^2}{16}=1 \\ Now a^2-b^2=-7<0 \\ For this hyperbola director circle doesn\text{'}t exist,so statement-I is false \end{gathered}$$

Statement-II:By conceptual the locus of point of intersection of perpendicular tangents lies on director circle

$\therefore$Statement-II is true.