Simultaneous elliptic equation x 2/4+y 2 = 1 ②

There are (4k2+1) x 2-8k2mx+4k2m2-4 = 0 ③.

Because the distance from the straight line to the origin is 1, according to the distance formula

lkml/√( 1+k^2)= 1

That is1+k 2/k 2 = m 2 4.

According to chord length formula

labl=√( 1+k^2)[(x 1+x2)^2-4x 1x2]

According to David's reasons ③ and ④, it can be concluded that.

lABl=4√3/(|m|+3/|m|)

So when |m|=3/|m|, the maximum value is 2.

So lABlmax=2

If you don't understand, ask again, for the lich king.