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
=1(a>b>0)的焦点F(c,0)的弦中最短弦长是( )y2 b2
A.
2b2
a
B.
2a2
b
C.
2c2
a
D.
2c2
b
答
由题意,过椭圆
+x2 a2
=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y2 b2
当x=c时,y=±
b2 a
∴最短弦长是
2b2
a
故选A.