已知?jiǎng)狱c(diǎn)Q到定點(diǎn)F
1(-1,0),F(xiàn)
2(1,0)的距離之和為4.
(1)求動(dòng)點(diǎn)Q的軌跡方程C;
(2)若軌跡C與直線y=x+m交于M,N兩點(diǎn),且
,求m的值;
(3)若點(diǎn)A(x
1,y
1)與點(diǎn)P(x
2,y
2)在軌跡C上,且點(diǎn)A在第一象限,點(diǎn)P在第二象限,點(diǎn)B與點(diǎn)A關(guān)于原點(diǎn)對(duì)稱,求證:當(dāng)
時(shí),三角形△PAB的面積為定值.