过椭圆C:x平方+2y平方=2的右焦点作直线l交椭圆于M、N两点,若M、N到直线X=2的距离和为10/3,求直线l的方程

x^2/2+y^2=1,c=1
准线x=a^2/c=2,直线X=2是准线,
根据椭圆第二定义MF/d=e=√2/2
M到直线X=2的距离d1=MF/e
N到直线X=2的距离d2=NF/e
10/3=MF/e+NF/e=(MF+NF)/e=MN/e
MN=5√2/3
设直线方程为y=k(x-1)
与椭圆方程联立得
(1+2k^2)x^2-4k^2x+2k^2-2=0
x1+x2=4k^2/(1+2k^2),
x1x2=(2k^2-2)/(1+2k^2)
MN=√(1+k^2)*|x1-x2|
=√(1+k^2)*√[(x1+x2)^2-4x1x2]
=√(1+k^2)*√[8(1+k^2)/(1+2k^2)^2]
=2√2(1+k^2)/(1+2k^2)
5√2/3=2√2(1+k^2)/(1+2k^2)
k^2=1/4,k=1/2或 k=-1/2
直线l的方程y=1/2(x-1)或y=-1/2(x-1)