Question

过椭圆x^2/a^2+y^2=1(a>1)的顶点B（0,-1）做椭圆的弦AB,求绝对值AB的最大值并求此时的A的坐标

Answer 1

设点A坐标为：（acosθ,sinθ),则

|AB|=√[(acosθ-0)^2+(sinθ+1)^2]

=√[a^2cos^2θ+sin^2θ++2sinθ+1]

=√[a^2(1-sin^2θ)+sin^2θ++2sinθ+1]

=√(1-a^2)sin^2θ+2sinθ+a^2+1]

=√(1-a^2)[sinθ-1/（a^2-1)]^2-1/(1-a^2)+a^2+1]

∵a>1

对a讨论：1)1