1.图像与x轴交于A(x1,0)B(x2,0)两点,则二次函数可表达为y = (x - x₁)(x - x₂)
= x² - (x₁ + x₂)x + x₁x₂
C(0,x₁x₂),且x₁x₂ < 0
tan∠BCO = |OB|/|OC| = |x₂|/|x₁x₂| = x₂/(-x₁x₂) = -1/x₁
∠BAC与AC的倾斜角互补,tan倾斜角 = tan(π - ∠BAC) = -tan∠BAC
tan倾斜角 = (x₁x₂ - 0)/(0-x₁) = -x₂
tan∠BAC = x₂ = tan∠BCO = -1/x₁
x₁x₂ = -1 = -m
m = 1
y = x² - 2x -1
2.EF + GH = FG = FH + GH
EF = FH
即F在抛物线的对称轴上.
y = x² - 2x -1 = (x - 1)² -2
对称轴:x = 1
圆D方程:(x - √2)² + y² =2
带入x = 1,t = y = √(2√2 -1) (-√(2√2 -1)< 0,舍去)