将直线l：y=x+m与椭圆9x²+16y²=144方程联立,消y得
9x^2+16(x+m)^2=144
9x^2+16(x^2+2mx+m^2)=144
25x^2+32mx+16m^2-144=0
（1）当直线与圆相切时,△=0
即(32m)^2-100(16m^2-144)=0
1024m^2-1600m^2+14400=0
-576m^2+14400=0
m^2=25
m=-5或m=5
（2）当直线与圆相交时,△＞0
即(32m)^2-100(16m^2-144)＞0
-5＜m＜5
（3）当直线与圆相离时,△＜0
即(32m)^2-100(16m^2-144)＜0
m＜-5或m＞5