This question has been asked before and the consensus was that parasailing is left untranslated in Spanish. I also found a site that called it vuelo por tiro

parapente = paragliding
ala delta = hang-gliding

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Note added at 15 mins (2003-12-12 22:03:06 GMT)
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Paragliding is also not Parasailing. Parasailing is done with a round parachute that is usually towed behind a boat. Unlike paragliding, the person being towed has little control over the parasail. Paragliding is not hang gliding. Hang gliders have a metal frame and fly in faster winds with the pilot steering by pushing and pulling on a metal bar.
http://www.overthehillparagliding.com/what.html

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Note added at 16 mins (2003-12-12 22:04:24 GMT)
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Another extract from the English link above:
What is paragliding?
Paragliding is a new flying sport which began in the French Alps during the mid 80\'s. The French call it PARAPENTE (pronounced para-pont). Paragliders, as we call them in the U.S. are loosely based on the ram-air, square parachutes that skydivers use