The Yagi consists of one driven element, plus one or more shorter elements acting as directors placed in front of it, plus one or more longer elements acting as reflectors placed behind it....
yagi udda antenna has only one reflector...but it has many directors...depending upon gain and efficiency...the length of reflector is normally...more than one-half of wavelength... and directors...
Yes, the Yagi-Uda antenna has several parasitic elements, in the form of a reflector ("behind" the driven element) and the directional elements ("in front" of the driven element).