已知抛物线y^2=4X上有三点,A(X1,Y1),B(X2,Y2),C(X3,Y3),斜率为Kab,Kac,Kbc.当X1取最小值时,求1/Kab+1/Kac+1/Kbc的值
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![已知抛物线y^2=4X上有三点,A(X1,Y1),B(X2,Y2),C(X3,Y3),斜率为Kab,Kac,Kbc.当X1取最小值时,求1/Kab+1/Kac+1/Kbc的值](/uploads/image/z/10232696-56-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D4X%E4%B8%8A%E6%9C%89%E4%B8%89%E7%82%B9%2CA%EF%BC%88X1%2CY1%29%2CB%28X2%2CY2%29%2CC%28X3%2CY3%29%2C%E6%96%9C%E7%8E%87%E4%B8%BAKab%2CKac%2CKbc.%E5%BD%93X1%E5%8F%96%E6%9C%80%E5%B0%8F%E5%80%BC%E6%97%B6%2C%E6%B1%821%2FKab%2B1%2FKac%2B1%2FKbc%E7%9A%84%E5%80%BC)
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已知抛物线y^2=4X上有三点,A(X1,Y1),B(X2,Y2),C(X3,Y3),斜率为Kab,Kac,Kbc.当X1取最小值时,求1/Kab+1/Kac+1/Kbc的值
已知抛物线y^2=4X上有三点,A(X1,Y1),B(X2,Y2),C(X3,Y3),斜率为Kab,Kac,Kbc.
当X1取最小值时,求1/Kab+1/Kac+1/Kbc的值
已知抛物线y^2=4X上有三点,A(X1,Y1),B(X2,Y2),C(X3,Y3),斜率为Kab,Kac,Kbc.当X1取最小值时,求1/Kab+1/Kac+1/Kbc的值
答:抛物线y^2=4x中,x>=0,所以X1取最小值0,Y1=0
点A(0,0),B(X2,Y2),C(X3,Y3)
Kab=Y2/X2=4/Y2
Kac=Y3/X3=4/Y3
Kbc=(Y3-Y2)/(X3-X2)
所以:
1/Kab+1/Kac+1/Kbc
=Y2/4+Y3/4+(X3-X2)/(Y3-Y2)
=(Y2+Y3)/4+(Y3^2/4-Y2^2/4)/(Y3-Y2)
=(Y2+Y3)/4+(Y2+Y3)/4
=(Y2+Y3)/2