c^2=16-4=12,设椭圆的标准方程X^2/（b^2+12)+Y^2/b^2=1,过点P(根号5,-根号6),则5/（b^2+12)+6/b^2=1,得b^2=8,椭圆的标准方程X^2/20+Y^2/8=1