c/a=根号2c=根号2*ac^2=a^2+b^2a^2=b^2∴a=b当焦点在x轴上时设x^2/a^2-y^2/a^2=1M代入得a=4∴x^2/16-y^2/16=1当焦点在y轴上时设y^2/a^2-x^2/a^2=1M代入得无解。∴综上，x^2/16-y^2/16=1为所求
