如图,在x轴上有两点A（m,0）,B（n,0）（n＞m＞0）．分别过点A,点B作x轴的垂线,交抛物线y=x2于点C、点D．直线OC交直线BD于点E,直线OD交直线AC于点F,点E、点F的纵坐标分别记为yE,yF．特例探究填空：当m=1,n=2时,yE=,yF=；当m=3,n=5时,yE=,yF=．归纳证明对任意m,n（n＞m＞0）,猜想yE与yF的大小关系,并证明你的猜想．拓展应用（1）若将“抛物
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m = 1, n = 2: yE = 2, yF = 2
m = 3, n = 5: yE = 15, yF = 15
M(m, m²), N(n, n²)
OM斜率: (m² - 0)/(m - 0) = m, 方程y = mx; 取x = n, y = mn, E(n, mn)
ON斜率: (n² - 0)/(n - 0) = n, 方程y = nx; 取x = m, y = mn, F(m, mn)
(1)M(m, am²), N(n, an²)
OM斜率: (am² - 0)/(m - 0) = am, 方程y = amx; 取x = n, y = amn, E(n, amn)
ON斜率: (an² - 0)/(n - 0) = an, 方程y = anx; 取x = m, y = amn, F(m, amn)
yE = yF(2)上面已得yE = yF, 四边形OFEB为梯形, 面积S = (1/2)(FE + OB)BE = (1/2)(n - m + n)mn
S△OFE = (1/2)FE*BE = (1/2)(n - m)mn
S四边形OFEB=3S△OFE, (1/2)(n - m + n)mn = (3/2)mn(n - m)
n = 2mEF = OA, 四边形OFEA为平行四边形