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

问题描述:

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/Y2Kac=Y3/X3=4/Y3Kbc=(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-Y...