Arithmetic progression, so AF2+BF2=2AB.

3AB=4 AB=4/3

(2) The linear equation is y=x+ root sign (1-m 2).

X 2+y 2/m 2 = 1 simultaneous.

Eliminate y gain

(1+m 2) x2-2 radical (1-m 2) x+(1-m 2) = 0.

Chord length formula

|AB|= radical sign (1+k 2) *| x2-x 1 |

4/3= radical number 2*|x2-x 1|

The number of 2 roots is 2/3=|x2-x 1|

8/9=x2^2-2x2x 1+x 1^2

x2^2-2x2x 1+x 1^2

=(x 1+x2)^2-4x 1x2

=4( 1-m^2)/( 1+m^2)^2-4( 1-2m^2)/( 1+m^2)

=8/9

arrange

8m^4-2m^2- 1=0

M 2 = 1/2 or m 2 =- 1/4 (omitted)

m^2= 1/2

M= root number 2/2