If the tangent at the point $(\mathrm{a} \sec \mathrm{\alpha }, \mathrm{b} \tan \mathrm{\alpha })$ to the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ meets the transverse axis at T, then the distance of T from a focus of the hyperbola is