$\text{ The chord of contact of the tangents drawn from a point on the circle }{x}^2+y^2=16$$\text{ with respect to the hyperbola }\frac{x^2}{16}-\frac{y^2}{9}=1\text{ always touches a conic whose eccentricity is }$

$\begin{array}{c}\text{ A point on }{x}^2+y^2=16\text{ be }p(4\cos \theta ,4\sin \theta )\\ \text{ The chord of contact of p w.r.t }\frac{x^2}{16}-\frac{y^2}{9}=1\text{ is }\frac{x}{16}\cdot 4\cos \theta -\frac{y}{9}\cdot 4\sin \theta =1\\ \Rightarrow \frac{x}{a}\cos \theta -\frac{y}{b}\sin \theta =1,\text{ where }a=4,b=\frac{9}{4}\text{ is a tangent to the ellipse }\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ e=\frac{5\sqrt{7}}{16}\end{array}$