The product of the lengths of the perpendiculars from any point of the hyperbola ${\mathrm{x}}^2-{\mathrm{y}}^2=8$ to its asymptotes is

$Given hyperbola x^2-y^2=8 where a^2=b^2=8$

Product of perpendiculars from any point on hyperbola to its asymptotes is $\frac{{\mathrm{a}}^2{\mathrm{b}}^2}{{\mathrm{a}}^2+{\mathrm{b}}^2}$

                                                                                                                                      =$\frac{8\left(8\right)}{16}=4$