直线l1:y=kx+1和l2:x+ky-1=0(其中k为参数,且|k|<1)的交点为p

直线l1:y=kx+1和l2:x+ky-1=0(其中k为参数,且|k|<1)的交点为p

|k|<1 ====> -1<k<1
y=kx+1

y=-x/k+1/k
交点为P
kx+1-1/k+x/k=0
kx+x/k-1/k+1=0
x(k+1/k)-1/k+1=0
x=(1/k-1)/(k+1/k)
x=[(1-k)/k] / [(k^2+1)/k]
x=(1-k)/(k^2+1)
|k|<1,k^2<1, (1-k)>0 k^2+1>0
y1=kx+1=(k-k^2)/(k^2+1)+1=(k-k^2+k^2+1)/(k^2+1)
y1=(k+1)/(k^2+1)

y2=-x/k+1/k= [-(1-k)/(k^2+1)+1]/k