(本小題滿分15分)
已知曲線
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,若按向量
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作平移變換得曲線

;若將曲線

按伸縮系數(shù)

向著
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軸作伸縮變換,再按伸縮系數(shù)3向著

軸作伸縮變換得到曲線

(1)求曲線

及

方程;
(2)若
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為
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上一點(diǎn),
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為
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上任意一點(diǎn),且

與曲線

相切(
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為切點(diǎn)),
求線段
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的最大值及對應(yīng)的
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點(diǎn)坐標(biāo).
(1)設(shè)曲線

上任意一點(diǎn)
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,
經(jīng)變換后曲線

上對應(yīng)點(diǎn)
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,設(shè)經(jīng)變換后曲線

上對應(yīng)點(diǎn)
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則由題知
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則

代入曲線

得

故曲線

的方程為

.o. ………….3分m
又

,則

代入曲線

得
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故曲線

的方程為

.o. ………….6分m
(2)設(shè)

,經(jīng)分析知要想
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最大,即
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到圓心距離

最大…….7分m
即

=
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=
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.o……...9分m
由

知

,即

, .o. ………….11分m
此時(shí)

,故

.o. ………….13分m
從而

.o. ………….15分m
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:

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
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
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
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
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為

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
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
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
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
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
與
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
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
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
、
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,則點(diǎn)
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的軌跡是 ( )

圓
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橢圓
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雙曲線
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拋物線
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的焦點(diǎn)為
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、
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,點(diǎn)

在雙曲線上且

軸,則

到直線
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的距離為 ( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
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是雙曲線
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的右支上一動點(diǎn),
F是雙曲線的右焦點(diǎn),已知
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,則
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的最小值是 ( )
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