(1)
OC = AB = √[(-2 - 0)² + (0 - 2)²] = 2√2
C(2√2, 0)
抛物线过A(-2, 0), C(2√2, 0), 可表达为y = -(x + 2)(x - 2√2) = -x² - 2(1- √2)x + 4√2
(2)
AO =OB, ∠OAE = 45˚
∠BEF = 180˚ - ∠OEF - ∠AEO = 180˚ - 45˚ - ∠AEO = 135˚ - ∠AEO (180˚: 平角)
∠AOE = 180˚ - ∠OAE - ∠AEO = 180˚ - 45˚ - ∠AEO = 135˚ - ∠AEO (180˚: ∆AOE内角和)
∠BEF = ∠AOE
(3)
AB的方程: x/(-2) + y/2 = 1, y = 2 + x
△EOF为等腰三角形时, 显然∠EOF不可能为90˚, 有两种可能：EF = EO或FE = FO
(i) EF = EO
∠OEF的平分线与OF垂直,而且平分OF, 此时平分线与x轴平行, OE, EF的斜率显然互为相反数
设E(e, 2 + e), 则F(0, 4 + 2e), -2 < e < 0
OE的斜率p = tan(45°/2) = sin45°/(1 + cos45°) = √2 - 1
EF的斜率q = -q = 1 - √2
OE的方程: y = (1 - √2)x
E(-√2, √2)
(ii)FE = FO
∠OEF = ∠FOE = 45°, EF与OF垂直
OE的斜率 = tan(90° + 45°) = -1
OE的方程: y = -x
与AB的交点为E(-1, 1)
(4)
(3)中的(ii)的结果EF与x轴平行, 这里不考虑.
E(-√2, √2), F(0, 2√2)
EF的方程: y = (√2 - 1)x + 2√2
y = 0, x = -2(√2 + 2), D(-2(√2 + 2), 0)
是△EDG面积的（2
2
+1）倍? 这是什么?