If I'm not mistaken, the light fixture shown is more of a bulb "holder" than a true reflector. Notice the flat surface of the bulb? I believe that is a spot light or flood light bulb which has its own reflector built in to it. The outer shape of the metal does not appear to be uniformly elliptical in shape. Of course, I could be wrong I've been messing with elliptical and parabolic shapes trying to come up with a simple, effective reflector and the shape of the one pictured does not seem to have enough "curvature" on the sides to be truly elliptical or parabolic. The search continues....
What he said. This fixture looks like it uses a PAR38 bulb, which is your typical run-of-the-mill residential floodlight bulb.
That is to say, the reflector is built into the bulb, so whether it's a flood (~25deg) or a spot (~15deg) depends on the bulb, not the fixture.
On the subject of reflectors, I recently ordered a PAR56 raylight reflector from partsexpress.com. It's a parabolic spotlight projector that's made to use a 600W halogen bulb (same hot hot hot bulb from some early OHPs). I was going to play around with it to see if I could mount a single-ended MH bulb in it. It's about 8" diam, but it's quite shallow so the standard 250-400W MHs won't work.