The ornamental design for a beautysalonchair with elliptically shaped back support, as shown and described.
FIG. 1 is a perspective view of a beauty salon chair with elliptically shaped back support showing my new design;
FIG. 2 is a top plan view of the beauty salon chair with elliptically shaped back support of FIG. 1;
FIG. 3 is a front elevational view of the beauty salon chair with elliptically shaped back support of FIG. 1;
FIG. 4 is a left side elevational view of the beauty salon chair with elliptically shaped back support of FIG. 1, with the opposite side being a mirror image of the side shown;
FIG. 5 is a back elevational view of the beauty salon chair with elliptically shaped back support of FIG. 1; and,
FIG. 6 is a bottom plan view of the beauty salon chair with elliptically shaped back support of FIG. 1.
The broken line showing the leg support in FIG. 1 is for illustrative purposes only and forms no part of the claimed design.