|PM|+|PN|=2√3
√[(x+1)²+y²]+√[(x-1)²+y²]=2√3
√[(x+1)²+y²]=2√3-√[(x-1)²+y²]
(x+1)²+y²=12-4√3√[(x-1)²+y²]+(x-1)²+y²
2x=12-4√3√[(x-1)²+y²]-2x
4x=12-4√3√[(x-1)²+y²]
√3√[(x-1)²+y²]=3-x
3(x-1)²+3y²=9-6x+x²
3x²-6x+3+3y²=9-6x+x²
2x²+3y²=6
x²/3+y²/2=1
所以p的轨迹C的方程x²/3+y²/2=1