  A subtracted dispersive representation of the $K\pi$ vector form factor,
$F_+^{K\pi}$, is used to fit the Belle spectrum of $\tauKpi$ decays
incorporating constraints from results on $K_{l3}$ decays. Through the use of
three subtractions, the slope and curvature of $F_+^{K\pi}$ are obtained
directly from the data yielding $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$
and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. The phase-space integrals
relevant for $K_{l3}$ analyses are calculated. Additionally, from the pole
position on the second Riemann sheet the mass and width of the $K^*(892)^\pm$
are found to be $m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and
$\Gamma_{K^*(892)^\pm}= 46.5 \pm 1.1$ MeV. Finally, we study the $P$-wave
isospin-1/2 $K\pi$ phase-shift and its threshold parameters.
