The locus of the point of intersection of perpendicular tangents to the hyperbola $\large\frac{x^{2}}{16}-\frac{y^{2}}{9}$=$1$ is

Question

$$\begin{array}{1 1} (1)x^{2}+y^{2}=25&(2)x^{2}+y^{2}=4\\(3)x^{2}+y^{2}=3&(4)x^{2}+y^{2}=7\end{array}$$