Can ethylparaben be detected by UV ? YES, you certainly should be able to detect it between 200 and 300 nm. It has a strong lambda max signal in that region which can be seen if you look at its chemical structure.

If you have solutions of 100% pure ethylparaben (not mixtures containing other compounds), then using standards, you could create a calibration curve using a UV/VIS spectrophotometer for qualitative measurements. If you have a mixture (solution) containing ethylparaben and other compounds, then NO, you probably can not use a UV/VIS spectrophotometer for analysis as it may not be selective for the compound due to the other compounds present in the solution.

Science teaches us that for a technique to be valid: the Analysis methods and techniques used must be selective for the specific compound. If you have other questions, please discuss with your chemistry teacher.