Consider the hyperbola
\[
S \equiv \frac{x^2}{25}-\frac{y^2}{16}-1=0.
\]
Let \(B,B'\) be the ends of the transverse axis of the conjugate hyperbola of \(S=0\). If \(C\) is the circle with \(B,B'\) as ends of a diameter, then the slope of a common tangent to \(C\) and the given hyperbola is: