Question

如图,过点B(0,-b)作椭圆 =1(a>b>0)的弦,求这些弦长的最大值.

Answer 1

|BM|的最大值为2b. 设M(x,y)是椭圆上任一点.|BM| 2 =x 2 +(y+b) 2 =x 2 +y 2 +2by+b 2 ,由 =1,有x 2 = (b 2 -y 2 ).将其代入上式,整理,然后配方有|BM| 2 =(1- )y 2 +2by+(a 2 +b 2 )=(1- )·(y- )...