(本小題滿分12分)
設(shè)圓
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的切線
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與兩坐標軸交于點
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.
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(1)證明:
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;
(2)若
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求△AOB的面積的最小值.
(1)設(shè)出直線
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的方程,用圓心到直線的距離等于圓半徑即可證明
(2)
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試題分析:(1)由已知得直線
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的方程為
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,即
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.
則圓心(2,2)到切線
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的距離
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,
即
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,
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.
(2)由
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又
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(當(dāng)且僅當(dāng)
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時取等號),所以,△AOB面積的最小值是
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點評:本題考查直線與圓的位置關(guān)系,考查基本不等式的運用,考查學(xué)生分析解決問題的能力,屬于中檔題.
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