题目内容
已知双曲线中心在原点,离心率为
,若它的一条准线与抛物线y2=4x的准线重合,则该双曲线与抛物线交点到原点的距离是( )
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A.2![]() ![]() | B.![]() | C.18+12![]() | D.21 |
B
抛物线的准线l:x=-1.对双曲线来说是其左准线,
∴-
=-1,
即a2=c.又离心率
=
,联立解得a=
,c=3,a2=3,b2=c2-a2=6,
∴双曲线
-
=1,联立y2=4x,解得x=3且y=±2
,
即交点P(3,±2
),
∴交点P到原点距离|OP|=
.
∴-
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即a2=c.又离心率
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∴双曲线
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即交点P(3,±2
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∴交点P到原点距离|OP|=
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