双曲线x平方/9-y平方/4=1与直线y=-2/3x+m的公共点的个数为

x²/9-y²/4=1 4x²-9y²=36; y=-2x/3+m ; 4x²-9y²=4x²-9(-2x/3+m)²=4x²-9(4x²/9-4xm/3+m²)=36;
4x²-4x²+12mx-9m²=36; 4mx-3m²=12; x=(12+3m²)/(4m);
所以:双曲线x²/9-y²/4=1与直线y=-2x/3+m的公共点的个数为1;