直线y=x+t代入得:
x^2+4(x+t)^2=4
x^2+4x^2+8xt+4t^2=4
5x^2+8tx+4t^2-4=0
x1+x2=-8t/5
x1x2=(4t^2-4)/5.
|x1-x2|^2=(x1+x2)^2-4x1x2=64t^2/25-16(t^2-1)/5=16(5-t^2)/25
设弦长是L
则L=根号(1+k^2)*|x1-x2|=根号(1+1)*|x1-x2|
即L^2=2*16(5-t^2)/25
当t=0时,L^2有最大值是L^2=32*5/25=32/5
即最大弦长是L=4根号10/5