设P(x,y)
PF1+PF2=2a
√(x+c)2+y2 + √(x-c)2+y2 =2a
(x+c)2+y2 =4a2-4a√(x-c)2+y2 +(x-c)2+y2
a2-cx=a √(x-c)2+y2
a^4-2a2cx+c2x2=a2x2-2a2cx+a2c2+a2y2
(a2-c2)x2+a2y2=a2(a2-c2)
因为a2-c2大于0
可设a2-c2=b2(b大于0)
所以b2x2+a2y2=a2b2
即x2/a2+y2/b2=1
设P(x,y)
PF1+PF2=2a
√(x+c)2+y2 + √(x-c)2+y2 =2a
(x+c)2+y2 =4a2-4a√(x-c)2+y2 +(x-c)2+y2
a2-cx=a √(x-c)2+y2
a^4-2a2cx+c2x2=a2x2-2a2cx+a2c2+a2y2
(a2-c2)x2+a2y2=a2(a2-c2)
因为a2-c2大于0
可设a2-c2=b2(b大于0)
所以b2x2+a2y2=a2b2
即x2/a2+y2/b2=1