distances (normalized to the $g$-band $25^{\rm th}$ magnitude isophotal semimajor axis; $R_{25}=D_{25}/2$) along major ($U/R_{25}$) and minor ($V/R_{25}$) axes would be the same both in face-on ($i \leq 60^\circ$) and in edge-on ($i > 60^\circ$) disc galaxies. The projected $U$ and $V$ galactocentric distances (in arcsec) of an SN are $$\begin{split}
 U = \Delta \alpha \,\sin {\rm PA} + \Delta \delta \,\cos {\rm PA} \ ,\\
 V = \Delta \alpha \,\cos {\rm PA} - \Delta \delta \,\sin {\rm PA} \ , \\
\end{split}
\label{UVdefs}$$ where $\Delta\alpha$ and $\Delta\delta$ are offsets of the SN in equatorial coordinate system, and PA is position angle of the major axis of the host galaxy. For more details of these formulae, the reader is referred to .

The $R_{25}$ normalization is important because the distribution of linear distances (in kpc) is strongly biased by the greatly different intrinsic sizes of host galaxies (see fig. 2 in ). In linear scale, there would be a systematic overpopulation of SNe at small galactocentric distances as this region would be populated by SNe exploding in all host galaxies, including the smaller ones, while larger distances would only be populated by the SNe occurring in the larger hosts.

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