Spatial offset between the BLR and continuum photocentres and its possible physical representation and their connection with optical AGN luminosity. (a) The BLR offset and (b) the flux ratio of two sides of the hot dust (W_r/W_l) as a function of optical AGN luminosity, assuming that the hot dust emits asymmetrically as explained in Sect. 10. The 4 targets introduced in this work are shown in circles, while the previously published AGNs (3C 273, IRAS 09149-6206, and NGC 3783) are shown in triangles. The error bars are 1σ errors calculated through the propagation of uncertainties from the centroid position of the null photocentre fitting. For comparison, the relation between hot dust size and AGN luminosity (Abuter et al. 2024) is shown by the red dashed line, while the relation between the BLR radius and AGN luminosity (the so-called R-L relation) based on Bentz et al. (2013) is shown by the blue dashed line. We also show the fitted R-L relation in this work depicted by the green dashed line. The Pearson correlation coefficients and p-values for the left and right plots are 0.81 and 0.026, and −0.15 and 0.73, respectively.