The Federal Energy Regulatory Commission on Thursday approved a $700 million floating liquefied-natural-gas terminal to be built in the middle of Long Island Sound. The energy companies Shell and TransCanada are partners in the project, which is expected to supply 1.25 billion cubic feet of natural gas a day to New York and Connecticut — enough to generate electricity for 4 million homes. Connecticut state officials and some environmentalists have been vocal opponents of the project, saying it would industrialize a popular recreation area and could become an attractive terrorist target. Connecticut’s attorney general called the terminal an “environmental atrocity” and vowed to fight the feds’ approval in court. The LNG terminal still needs approval from two New York state agencies to proceed.