过椭圆x2a2+y2b2=1(a>b>0)的焦点F(c,0)的弦中最短弦长是(  ) A.2b2a B.2a2b C.2c2a D.2c2b

问题描述:

过椭圆

x2
a2
+
y2
b2
=1(a>b>0)的焦点F(c,0)的弦中最短弦长是(  )
A.
2b2
a

B.
2a2
b

C.
2c2
a

D.
2c2
b

由题意,过椭圆

x2
a2
+
y2
b2
=1(a>b>0)的焦点F(c,0)的弦中最短弦为过焦点垂直于x轴弦
当x=c时,y=±
b2
a

∴最短弦长是
2b2
a

故选A.