易求得平移后：y=[x+2m/(m²+1)]²+(m²-1)/(m²+1),
令m²=k,则a=(k²+4k-1)/(k²+2k+1),
整理得：(a-1)k²+2(a-2)k+(a+1)=0,
判别式 4(a-2)²-4(a-1)(a+1)=4(5-4a)≥0,
解得：a≤5/4,即：a最大值为5/4.