问题
选择题
设AB为抛物线y2=x上的动弦,且|AB|=2,则弦AB的中点M到y轴的最小距离为( )
|
答案
由题意,抛物线y2=x的焦点坐标为(
,0),准线方程为x=-1 4
.1 4
根据抛物线的定义,∵|AB|=2,∴A、B到准线的距离和最小为2(当且仅当A,B,F三点共线时取最小)
∴弦AB的中点到准线的距离最小为1
∴弦AB的中点到y轴的最小距离为1-
=1 4
.3 4
故选B.
设AB为抛物线y2=x上的动弦,且|AB|=2,则弦AB的中点M到y轴的最小距离为( )
|
由题意,抛物线y2=x的焦点坐标为(
,0),准线方程为x=-1 4
.1 4
根据抛物线的定义,∵|AB|=2,∴A、B到准线的距离和最小为2(当且仅当A,B,F三点共线时取最小)
∴弦AB的中点到准线的距离最小为1
∴弦AB的中点到y轴的最小距离为1-
=1 4
.3 4
故选B.
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