(20 12 Wenzhou) parabola passing through the origin Y =-x2+2mx (m >); 0) and the other intersection of the X axis is a. The passing point P( 1, m) is a straight line PM⊥x axis is at the point.

I don't know if you still need it. . .

∵B and C are not coincident ∴m≠ 1

① When m= 1, BC=2(m- 1), PM=m, BP=m- 1.

(I) if point e is on the x axis

∠∠CPE = 90

∴∠MPE+∠BPC=∠MPE+∠MEP=90，PC=EP

∴△BPC≌△MEP

∴BC=PM？ ∴2(m- 1)=m？ ∴m=2

At this time, the coordinate of point E is (2,0).

(ii) if point e is on the y axis.

The passing point p is PN⊥y axis and point n.

Yi Zheng △ BPC △ NPE

∴bp=np=om= 1 ∴m- 1= 1 ∴m=2

At this time, the coordinates of point E are (0,4).

② when 0 < m < 1, BC = 2 (1-m), PM = m, BP =1-m.

(I) if point e is on the x axis

Yi Zheng △ BPC △ MEP ∴ BC = pm ∴ 2 (1-m) = m ∴ m = 2/3.

At this time, the coordinate of point E is (4/3,0).

(ii) if point e is on the y axis.

The passing point p is PN⊥y axis and point n.

Yi Zheng △ BPC △ NPE? ∴ BP = NP = OM =1∴1-m =1∴ m = 0 (omitted)

To sum up, when m=2, the coordinates of point E are (0,2) or (0,4).

When m=2 /3, the coordinate of point E is (4/3,0).