|F1F2|=2c>0,設(shè)F1,F2的坐標(biāo)分別為F1(-c,0),F2(c,0).
C上任意一點(diǎn)P的坐標(biāo)為(x,y):
|CF1|^2 + |CF2|^2 = 2a^2
|CF1|^2 = (x+c)^2 + y^2
|CF2|^2 = (x-c)^2 + y^2
(x+c)^2 + y^2 + (x-c)^2 + y^2 = 2a^2
簡(jiǎn)化得:x^2 + y^2 = a^2 - c^2
a < c時(shí),a^2 - c^2 < 0,曲線C不存在
a = c時(shí),a^2 - c^2 = 0,曲線C是原點(diǎn)
a > c時(shí),a^2 - c^2 > 0,曲線C是以原點(diǎn)為圓心,半徑為sqrt(a^2-c^2)的圓 (sqrt為平方根).