It wouldn't be a great thing, if you could find a path to that profile or page from where you have downloaded a image from a long time ago. You can do it within a few clicks. I will show you, how will you come to know that profile or page from that photo. Don't forget to check my previous post How to view private profile picture of a Facebook ProfileNumber 2:
So, here we go...
STEP 1: Copy the image file name.
STEP 2: Image file name would be like: number1_number2_number3_n.jpg
STEP 3: Copy the number2 carefully from file name.
STEP 4: Paste that number to the following input box.
STEP 5: You will be redirected to Image's album, then you can simply find that whose profile it was. You have done it.! ;)