課時規(guī)范練55直線與圓錐曲線的位置關(guān)系高考總復(fù)習(xí)優(yōu)化設(shè)計GAOKAOZONGFUXIYOUHUASHEJI2026基礎(chǔ)鞏固練12345678910111213141516

B

123456789101112131415162.直線x+y+2=0與拋物線C:y2=ax(a≠0)的圖象相切,則C的準(zhǔn)線方程為(

)A.x=-2 B.x=-1C.y=-2 D.y=-1A

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D12345678910111213141516

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C

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B12345678910111213141516

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123456789101112131415169.(2024·江西宜春三模)已知拋物線C:y2=4x的焦點(diǎn)為F,動直線l與拋物線C交于異于原點(diǎn)O的A,B兩點(diǎn),以線段OA,OB為鄰邊作平行四邊形OAPB,若點(diǎn)P(4,m)(m>0),則當(dāng)|AB|取最大值時,m的值為

.

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綜合提升練A12345678910111213141516

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D

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ABC12345678910111213141516

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12345678910111213141516(方法二)設(shè)線段F1M的垂直平分線l與C恰有一個公共點(diǎn)為P,則當(dāng)點(diǎn)P不在長軸時,線段F1M的垂直平分線l即為點(diǎn)P處C的切線,也為∠F1PM的角平分線,作∠F1PF2的角平分線PH,根據(jù)橢圓的性質(zhì)易知PH⊥l,所以∠F1PE+∠F1PH=90°,則∠F2PH+∠EPM=90°,故∠F2PF1+∠F1PM=180°,所以M,P,F2三點(diǎn)共線,所以|MF2|=|MP|+|PF2|=|PF1|+|PF2|=4,所以點(diǎn)M的軌跡是以F2為圓心,4為半徑的圓,當(dāng)P在橢圓長軸上時,點(diǎn)M為(5,0)或(-3,0),也滿足|MF2|=4,故點(diǎn)M的軌跡是圓,該圓的方程為(x-1)2+y2=16.12345678910111213141516