y=kx+2
与y=x^2 联立
x^2-kx-2=0
△=k^2+8>0 k2√2
x1=0.5k-√2 x2=0.5k+√2
y1=0.5k^2-√2k+2 y2=0.5k^2+√2k+2
M(0.5k-√2,0.5k^2-√2k+2 )
N(0.5k+√2,0.5k^2+√2k+2)
y=x^2求导 y'=2x
过M N分别作抛物线的切线
M处切线斜率=2(0.5k-√2)=k-2√2
N处切线斜率=2(0.5k+√2)=k+2√2
过M点L1:y-(0.5k^2-√2k+2)=(k-2√2) (x-0.5k+√2)
过N点L2:y-(0.5k^2+√2k+2)=(k+2√2) (x-0.5k-√2)
二者交点 (k/2,0.5k^2+2√2k-6)
轨迹为 y=0.5(2x)^2+2√2*2x-6=2x^2+4√2x-6
∵k2√2
x4√2