(1)略
(2)设直线方程:y=kx+√2,代入椭圆方程得(1/4+k²)x²+2√2kx+1=0,所以x1+x2=-2√2k/(1/4+k²)
即√2k/(1/4+k²)=4√2/5,解得k1=1,k2=1/4