设过抛物线的焦点F的弦为PQ,则以PQ为直径的圆与此抛物线的准线的位

设过抛物线的焦点F的弦为PQ,则以PQ为直径的圆与此抛物线的准线的位置关系是(    )

A.相交       B.相切       C.相离      D.以上答案均有可能

答案

解析:过点P、Q分别作准线的垂线PP1、QQ1,其中P1、Q1为垂足.由抛物线的定义|PP1|+|QQ1|=|PF|+|FQ|=|PQ|.

∴直径PQ的中点到准线的距离d=(|PP1|+|QQ1|)=|PQ|,即圆心到准线的距离等于半径.∴相切.

答案:B

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