题目内容
已知一组抛物线
,其中
为2、4、6、8中任取的一个数,
为1、3、5、7中任取的一个数,从这些抛物线中任意抽取两条,它们在与直线
交点处的切线相互平行的概率是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
B
选B.这一组抛物线共
条,从中任意抽取两条,共有
种不同的方法.它们在与直线
交点处的切线的斜率
.若
,有两种情形,从中取出两条,有
种取法;若
,有三种情形,从中取出两条,有
种取法;若
,有四种情形,从中取出两条,有
种取法;若
,有三种情形,从中取出两条,有
种取法;若
,有两种情形,从中取出两条,有
种取法.由分类计数原理知任取两条切线平行的情形共有
种,故所求概率为
.
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