新高考數(shù)學(xué)二輪復(fù)習(xí) 多選題分類(lèi)提升練習(xí)專(zhuān)題五【解析幾何】多選題專(zhuān)練六十題（原卷版）

多選題專(zhuān)練六十題專(zhuān)題五解析幾何（學(xué)生版）第一部——高考真題練1．（2023·全國(guó)·統(tǒng)考高考真題）設(shè)O為坐標(biāo)原點(diǎn)，直線SKIPIF1<0過(guò)拋物線SKIPIF1<0的焦點(diǎn)，且與C交于M，N兩點(diǎn)，l為C的準(zhǔn)線，則（

）．A．SKIPIF1<0 B．SKIPIF1<0C．以MN為直徑的圓與l相切 D．SKIPIF1<0為等腰三角形2．（2022·全國(guó)·統(tǒng)考高考真題）已知O為坐標(biāo)原點(diǎn)，過(guò)拋物線SKIPIF1<0焦點(diǎn)F的直線與C交于A，B兩點(diǎn)，其中A在第一象限，點(diǎn)SKIPIF1<0，若SKIPIF1<0，則（

）A．直線SKIPIF1<0的斜率為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·統(tǒng)考高考真題）雙曲線C的兩個(gè)焦點(diǎn)為SKIPIF1<0，以C的實(shí)軸為直徑的圓記為D，過(guò)SKIPIF1<0作D的切線與C交于M，N兩點(diǎn)，且SKIPIF1<0，則C的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·統(tǒng)考高考真題）已知O為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，過(guò)點(diǎn)SKIPIF1<0的直線交C于P，Q兩點(diǎn)，則（

）A．C的準(zhǔn)線為SKIPIF1<0 B．直線AB與C相切C．SKIPIF1<0 D．SKIPIF1<05．（2021·全國(guó)·統(tǒng)考高考真題）已知直線SKIPIF1<0與圓SKIPIF1<0，點(diǎn)SKIPIF1<0，則下列說(shuō)法正確的是（

）A．若點(diǎn)A在圓C上，則直線l與圓C相切 B．若點(diǎn)A在圓C內(nèi)，則直線l與圓C相離C．若點(diǎn)A在圓C外，則直線l與圓C相離 D．若點(diǎn)A在直線l上，則直線l與圓C相切6．（2021·全國(guó)·統(tǒng)考高考真題）已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，點(diǎn)SKIPIF1<0、SKIPIF1<0，則（

）A．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離小于SKIPIF1<0B．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離大于SKIPIF1<0C．當(dāng)SKIPIF1<0最小時(shí)，SKIPIF1<0D．當(dāng)SKIPIF1<0最大時(shí)，SKIPIF1<07．（2020·海南·高考真題）已知曲線SKIPIF1<0.（

）A．若m>n>0，則C是橢圓，其焦點(diǎn)在y軸上B．若m=n>0，則C是圓，其半徑為SKIPIF1<0C．若mn<0，則C是雙曲線，其漸近線方程為SKIPIF1<0D．若m=0，n>0，則C是兩條直線第二部——基礎(chǔ)模擬題8．（2023·海南?？凇ずＤ先A僑中學(xué)校考二模）已知橢圓SKIPIF1<0的上頂點(diǎn)為SKIPIF1<0，兩個(gè)焦點(diǎn)為SKIPIF1<0，離心率為SKIPIF1<0．過(guò)SKIPIF1<0且垂直于SKIPIF1<0的直線與SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的周長(zhǎng)是26，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．直線SKIPIF1<0的斜率為SKIPIF1<0 D．SKIPIF1<09．（2023·廣東深圳·統(tǒng)考二模）如圖，雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，過(guò)SKIPIF1<0向圓SKIPIF1<0作一條切線SKIPIF1<0與漸近線SKIPIF1<0和SKIPIF1<0分別交于點(diǎn)SKIPIF1<0（SKIPIF1<0恰好為切點(diǎn)，且是漸近線與圓的交點(diǎn)），設(shè)雙曲線的離心率為SKIPIF1<0.當(dāng)SKIPIF1<0時(shí)，下列結(jié)論正確的是（

）

A．SKIPIF1<0B．SKIPIF1<0C．當(dāng)點(diǎn)SKIPIF1<0在第一象限時(shí)，SKIPIF1<0D．當(dāng)點(diǎn)SKIPIF1<0在第三象限時(shí)，SKIPIF1<010．（2023·福建福州·福建省福州第一中學(xué)?？寄M預(yù)測(cè)）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，直線SKIPIF1<0過(guò)SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，SKIPIF1<0在拋物線SKIPIF1<0的準(zhǔn)線上的投影分別為SKIPIF1<0，若SKIPIF1<0與SKIPIF1<0的面積比為SKIPIF1<0，則下列說(shuō)法錯(cuò)誤的是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0與SKIPIF1<0的外接圓半徑之比為SKIPIF1<0D．直線SKIPIF1<0上存在兩個(gè)點(diǎn)SKIPIF1<0使得SKIPIF1<011．（2023·海南省直轄縣級(jí)單位·文昌中學(xué)?？寄M預(yù)測(cè)）已知圓SKIPIF1<0和圓SKIPIF1<0的交點(diǎn)為SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，則下列結(jié)論正確的是（

）A．直線SKIPIF1<0的方程為SKIPIF1<0B．圓SKIPIF1<0上存在兩點(diǎn)SKIPIF1<0和SKIPIF1<0，使得SKIPIF1<0C．圓SKIPIF1<0上的點(diǎn)到直線SKIPIF1<0的最大距離為SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0或SKIPIF1<012．（2023·廣東茂名·茂名市第一中學(xué)校考三模）我國(guó)首先研制成功的“雙曲線新聞燈”，如圖，利用了雙曲線的光學(xué)性質(zhì)：SKIPIF1<0，SKIPIF1<0是雙曲線的左?右焦點(diǎn)，從SKIPIF1<0發(fā)出的光線SKIPIF1<0射在雙曲線右支上一點(diǎn)SKIPIF1<0，經(jīng)點(diǎn)SKIPIF1<0反射后，反射光線的反向延長(zhǎng)線過(guò)SKIPIF1<0；當(dāng)SKIPIF1<0異于雙曲線頂點(diǎn)時(shí)，雙曲線在點(diǎn)SKIPIF1<0處的切線平分SKIPIF1<0.若雙曲線SKIPIF1<0的方程為SKIPIF1<0，則下列結(jié)論正確的是（

）

A．射線SKIPIF1<0所在直線的斜率為SKIPIF1<0，則SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0時(shí)，光線由SKIPIF1<0到SKIPIF1<0再到SKIPIF1<0所經(jīng)過(guò)的路程為13D．若點(diǎn)SKIPIF1<0坐標(biāo)為SKIPIF1<0，直線SKIPIF1<0與SKIPIF1<0相切，則SKIPIF1<013．（2023·河北衡水·衡水市第二中學(xué)?？既＃┮阎€SKIPIF1<0是頂點(diǎn)分別為SKIPIF1<0的雙曲線，點(diǎn)SKIPIF1<0（異于SKIPIF1<0）在SKIPIF1<0上，則（

）A．SKIPIF1<0B．SKIPIF1<0的焦點(diǎn)為SKIPIF1<0C．SKIPIF1<0的漸近線可能互相垂直D．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0的斜率之積為114．（2023·山東菏澤·山東省鄄城縣第一中學(xué)?？既＃┮阎c(diǎn)SKIPIF1<0，SKIPIF1<0動(dòng)點(diǎn)SKIPIF1<0滿(mǎn)足SKIPIF1<0，則下面結(jié)論正確的為（

）A．點(diǎn)SKIPIF1<0的軌跡方程為SKIPIF1<0 B．點(diǎn)SKIPIF1<0到原點(diǎn)SKIPIF1<0的距離的最大值為5C．SKIPIF1<0面積的最大值為4 D．SKIPIF1<0的最大值為1815．（2023·廣東佛山·統(tǒng)考模擬預(yù)測(cè)）已知雙曲線SKIPIF1<0：SKIPIF1<0上、下焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，虛軸長(zhǎng)為SKIPIF1<0，SKIPIF1<0是雙曲線上支上任意一點(diǎn)，SKIPIF1<0的最小值為SKIPIF1<0.設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是直線SKIPIF1<0上的動(dòng)點(diǎn)，直線SKIPIF1<0，SKIPIF1<0分別與E的上支交于點(diǎn)SKIPIF1<0，SKIPIF1<0，設(shè)直線SKIPIF1<0，SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0.下列說(shuō)法中正確的是（

）A．雙曲線SKIPIF1<0的方程為SKIPIF1<0 B．SKIPIF1<0C．以SKIPIF1<0為直徑的圓經(jīng)過(guò)SKIPIF1<0點(diǎn) D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0平行于SKIPIF1<0軸16．（2023·廣東廣州·廣州市從化區(qū)從化中學(xué)?？寄M預(yù)測(cè)）設(shè)SKIPIF1<0，過(guò)定點(diǎn)SKIPIF1<0的直線SKIPIF1<0與過(guò)定點(diǎn)SKIPIF1<0的直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0，線段SKIPIF1<0是圓SKIPIF1<0的一條動(dòng)弦，且SKIPIF1<0，給出下列四個(gè)結(jié)論：其中所有正確結(jié)論的序號(hào)是（

）A．SKIPIF1<0一定垂直SKIPIF1<0B．SKIPIF1<0的最大值為4C．點(diǎn)SKIPIF1<0的軌跡方程為SKIPIF1<0D．SKIPIF1<0的最小值為SKIPIF1<017．（2023·河北滄州·?？寄M預(yù)測(cè)）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0與該拋物線交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0的最小值為4，SKIPIF1<0為坐標(biāo)原點(diǎn)，則（

）A．SKIPIF1<0B．存在直線SKIPIF1<0，使得SKIPIF1<0的面積為1C．對(duì)于任意的直線SKIPIF1<0，都有SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0的傾斜角為SKIPIF1<0或SKIPIF1<018．（2023·福建福州·福建省福州第一中學(xué)校考模擬預(yù)測(cè)）拋物線有如下光學(xué)性質(zhì)：從焦點(diǎn)發(fā)出的光線經(jīng)拋物線反射后，沿平行于拋物線對(duì)稱(chēng)軸的方向射出；反之，平行于拋物線對(duì)稱(chēng)軸的入射光線經(jīng)拋物線反射后，必過(guò)拋物線的焦點(diǎn).已知平行于SKIPIF1<0軸的光線SKIPIF1<0從點(diǎn)SKIPIF1<0射入，經(jīng)過(guò)拋物線SKIPIF1<0上的點(diǎn)SKIPIF1<0反射，再經(jīng)過(guò)SKIPIF1<0上另一點(diǎn)SKIPIF1<0反射后，沿直線SKIPIF1<0射出，經(jīng)過(guò)點(diǎn)SKIPIF1<0，則（

）

A．若SKIPIF1<0的方程為SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0的方程為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0C．分別延長(zhǎng)SKIPIF1<0交于點(diǎn)SKIPIF1<0，則點(diǎn)SKIPIF1<0在SKIPIF1<0的準(zhǔn)線上D．拋物線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線分別與直線SKIPIF1<0，SKIPIF1<0所成角相等19．（2023·福建福州·福建省福州第一中學(xué)?？级＃佄锞€SKIPIF1<0為定值SKIPIF1<0焦點(diǎn)為SKIPIF1<0，SKIPIF1<0與直線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為SKIPIF1<0中點(diǎn).過(guò)SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為SKIPIF1<0，過(guò)SKIPIF1<0作SKIPIF1<0的垂線，交SKIPIF1<0軸于SKIPIF1<0，則（

）A．SKIPIF1<0B．SKIPIF1<0的縱坐標(biāo)是定值C．SKIPIF1<0為定值D．存在唯一的SKIPIF1<0使得SKIPIF1<020．（2023·廣東·校聯(lián)考模擬預(yù)測(cè)）已知橢圓SKIPIF1<0的焦點(diǎn)在SKIPIF1<0軸上，且SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為橢圓SKIPIF1<0上一點(diǎn)，則下列結(jié)論正確的是（

）A．SKIPIF1<0B．SKIPIF1<0的離心率為SKIPIF1<0C．存在SKIPIF1<0，使得SKIPIF1<0D．SKIPIF1<0面積的最大值為SKIPIF1<021．（2023·福建漳州·統(tǒng)考模擬預(yù)測(cè)）上甘嶺戰(zhàn)役是抗美援朝中中國(guó)人民志愿軍進(jìn)行的最著名的山地防御戰(zhàn)役.在這場(chǎng)戰(zhàn)役中，我軍使用了反斜面陣地防御戰(zhàn)術(shù).反斜面是山地攻防戰(zhàn)斗中背向敵方、面向我方的一側(cè)山坡.反斜面陣地的構(gòu)建，是為了規(guī)避敵方重火力輸出.某反斜面陣地如圖所示，山腳SKIPIF1<0，SKIPIF1<0兩點(diǎn)和敵方陣地SKIPIF1<0點(diǎn)在同一條直線上，某炮彈的彈道SKIPIF1<0是拋物線SKIPIF1<0的一部分，其中SKIPIF1<0在直線SKIPIF1<0上，拋物線的頂點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為100米，SKIPIF1<0長(zhǎng)為400米，SKIPIF1<0，SKIPIF1<0，建立適當(dāng)?shù)淖鴺?biāo)系使得拋物線SKIPIF1<0的方程為SKIPIF1<0，則（

）

A．SKIPIF1<0 B．SKIPIF1<0的準(zhǔn)線方程為SKIPIF1<0C．SKIPIF1<0的焦點(diǎn)坐標(biāo)為SKIPIF1<0 D．彈道SKIPIF1<0上的點(diǎn)到直線SKIPIF1<0的距離的最大值為SKIPIF1<022．（2023·重慶·統(tǒng)考模擬預(yù)測(cè)）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作x軸的垂線與雙曲線交于A，B兩點(diǎn)，若SKIPIF1<0為直角三角形，則（

）A．SKIPIF1<0B．雙曲線的離心率SKIPIF1<0C．雙曲線的焦距為SKIPIF1<0D．SKIPIF1<0的面積為SKIPIF1<023．（2023·遼寧·遼寧實(shí)驗(yàn)中學(xué)?？寄M預(yù)測(cè)）已知點(diǎn)M，N在圓O：SKIPIF1<0上運(yùn)動(dòng)，點(diǎn)SKIPIF1<0，且SKIPIF1<0，Q為線段M，N的中點(diǎn)，則（

）A．過(guò)點(diǎn)P有且只有一條直線與圓O相切B．SKIPIF1<0C．點(diǎn)Q在直線SKIPIF1<0上運(yùn)動(dòng)D．SKIPIF1<0的最大值為SKIPIF1<024．（2023·廣東廣州·華南師大附中?？既＃┰谄矫嬷苯亲鴺?biāo)系SKIPIF1<0中，雙曲線SKIPIF1<0：SKIPIF1<0的下、上焦點(diǎn)分別是SKIPIF1<0，SKIPIF1<0，漸近線方程為SKIPIF1<0，SKIPIF1<0為雙曲線SKIPIF1<0上任意一點(diǎn)，SKIPIF1<0平分SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則（

）A．雙曲線SKIPIF1<0的離心率為SKIPIF1<0B．雙曲線SKIPIF1<0的方程為SKIPIF1<0C．若直線SKIPIF1<0與雙曲線SKIPIF1<0的另一個(gè)交點(diǎn)為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的中點(diǎn)，則SKIPIF1<0D．點(diǎn)SKIPIF1<0到兩條漸近線的距離之積為SKIPIF1<025．（2023·遼寧錦州·渤海大學(xué)附屬高級(jí)中學(xué)?？寄M預(yù)測(cè)）已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0與雙曲線SKIPIF1<0：SKIPIF1<0的公共焦點(diǎn)，SKIPIF1<0，SKIPIF1<0分別是SKIPIF1<0與SKIPIF1<0的離心率，且P是SKIPIF1<0與SKIPIF1<0的一個(gè)公共點(diǎn)，滿(mǎn)足SKIPIF1<0，則下列結(jié)論中正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的最小值為SKIPIF1<0 D．SKIPIF1<0的最大值為SKIPIF1<026．（2023·山東泰安·統(tǒng)考模擬預(yù)測(cè)）已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0的直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0，直線SKIPIF1<0左邊的拋物線上存在一點(diǎn)SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．若點(diǎn)SKIPIF1<0，則SKIPIF1<0 D．當(dāng)SKIPIF1<0的面積最大時(shí)，面積為SKIPIF1<027．（2023·吉林·長(zhǎng)春吉大附中實(shí)驗(yàn)學(xué)校?？寄M預(yù)測(cè)）如圖，雙曲線E：SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)SKIPIF1<0的直線l與其右支交于P，Q兩點(diǎn)，已知SKIPIF1<0且SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0B．雙曲線的離心率為2C．SKIPIF1<0D．SKIPIF1<0的面積為SKIPIF1<028．（2023·吉林通化·梅河口市第五中學(xué)?？寄M預(yù)測(cè)）已知點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0與拋物線交于SKIPIF1<0兩點(diǎn)，拋物線SKIPIF1<0的準(zhǔn)線與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，下列說(shuō)法正確的是（

）A．若SKIPIF1<0過(guò)拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，則直線SKIPIF1<0斜率之積為定值B．若拋物線上的點(diǎn)SKIPIF1<0到點(diǎn)SKIPIF1<0的距離為4，則拋物線的方程為SKIPIF1<0C．以SKIPIF1<0為直徑的圓與準(zhǔn)線相切D．直線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0且交SKIPIF1<0于不同的SKIPIF1<0兩點(diǎn)，則SKIPIF1<029．（2023·吉林長(zhǎng)春·長(zhǎng)春吉大附中實(shí)驗(yàn)學(xué)校?？寄M預(yù)測(cè)）設(shè)SKIPIF1<0，圓SKIPIF1<0（SKIPIF1<0為圓心），SKIPIF1<0為圓SKIPIF1<0上任意一點(diǎn)，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作線段SKIPIF1<0的垂線與直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0．當(dāng)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)時(shí)，點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0，點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0，則下列說(shuō)法正確的有（

）A．曲線SKIPIF1<0的方程為SKIPIF1<0 B．當(dāng)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上時(shí)，點(diǎn)SKIPIF1<0的橫坐標(biāo)為SKIPIF1<0C．曲線SKIPIF1<0的方程為SKIPIF1<0 D．SKIPIF1<0與SKIPIF1<0無(wú)公共點(diǎn)30．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）拋物線SKIPIF1<0的準(zhǔn)線方程為SKIPIF1<0，過(guò)焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則（

）A．SKIPIF1<0的方程為SKIPIF1<0B．SKIPIF1<0的最小值為SKIPIF1<0C．過(guò)點(diǎn)SKIPIF1<0且與拋物線僅有一個(gè)公共點(diǎn)的直線有且僅有2條D．過(guò)點(diǎn)SKIPIF1<0分別作SKIPIF1<0的切線，交于點(diǎn)SKIPIF1<0，則直線SKIPIF1<0的斜率滿(mǎn)足SKIPIF1<031．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）雙曲線SKIPIF1<0的左、右焦點(diǎn)分別SKIPIF1<0，具有公共焦點(diǎn)的橢圓與雙曲線在第一象限的交點(diǎn)為SKIPIF1<0，雙曲線和橢圓的離心率分別為SKIPIF1<0的內(nèi)切圓的圓心為SKIPIF1<0，過(guò)SKIPIF1<0作直線SKIPIF1<0的垂線，垂足為SKIPIF1<0，則（

）A．SKIPIF1<0到SKIPIF1<0軸的距離為SKIPIF1<0B．點(diǎn)SKIPIF1<0的軌跡是雙曲線C．若SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<032．（2023·江蘇蘇州·模擬預(yù)測(cè)）在平面直角坐標(biāo)系SKIPIF1<0中，已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0且傾斜角為SKIPIF1<0的直線SKIPIF1<0分別交SKIPIF1<0的左、右兩支于點(diǎn)SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，連接SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<033．（2023·湖南·校聯(lián)考模擬預(yù)測(cè)）已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，圓C：SKIPIF1<0，下列說(shuō)法正確的是（

）A．若SKIPIF1<0經(jīng)過(guò)圓心C，則SKIPIF1<0B．直線SKIPIF1<0與圓C相離C．若SKIPIF1<0，且它們之間的距離為SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，SKIPIF1<0與圓C相交于M，N，則SKIPIF1<034．（2023·湖南邵陽(yáng)·邵陽(yáng)市第二中學(xué)校考模擬預(yù)測(cè)）已知圓SKIPIF1<0，圓SKIPIF1<0，直線SKIPIF1<0，則下列說(shuō)法正確的是（

）A．圓SKIPIF1<0的圓心為SKIPIF1<0B．圓SKIPIF1<0與圓SKIPIF1<0有四條公切線C．點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則線段SKIPIF1<0長(zhǎng)的最大值為SKIPIF1<0D．直線SKIPIF1<0與圓SKIPIF1<0一定相交，且相交的弦長(zhǎng)最小值為SKIPIF1<035．（2023·黑龍江哈爾濱·哈爾濱市第六中學(xué)校校考三模）在平面直角坐標(biāo)系xOy中，已知定點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)P滿(mǎn)足SKIPIF1<0，記動(dòng)點(diǎn)P的軌跡為曲線C，直線l：SKIPIF1<0，則下列結(jié)論中正確的是（

）A．曲線C的方程為SKIPIF1<0B．直線l與曲線C相交C．若直線l被曲線C截得的弦長(zhǎng)為SKIPIF1<0，則SKIPIF1<0D．SKIPIF1<0的最大值為336．（2023·山東煙臺(tái)·統(tǒng)考三模）在正四棱柱SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0滿(mǎn)足SKIPIF1<0，SKIPIF1<0，則（

）A．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0與SKIPIF1<0所成角為SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最小值為SKIPIF1<0C．若SKIPIF1<0與平面SKIPIF1<0所成角為SKIPIF1<0，則SKIPIF1<0點(diǎn)的軌跡長(zhǎng)為SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，平面SKIPIF1<0截此正四棱柱所得截面的最大面積為SKIPIF1<037．（2023·山東煙臺(tái)·統(tǒng)考三模）已知點(diǎn)SKIPIF1<0為直線SKIPIF1<0與SKIPIF1<0軸交點(diǎn)，SKIPIF1<0為圓SKIPIF1<0上的一動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0，則（

）A．SKIPIF1<0取得最小值時(shí)，SKIPIF1<0 B．SKIPIF1<0與圓SKIPIF1<0相切時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 D．SKIPIF1<0的最大值為SKIPIF1<038．（2023·廣東深圳·?？级＃┮阎獟佄锞€C的方程為SKIPIF1<0，過(guò)C焦點(diǎn)F的直線與C交于M，N兩點(diǎn)，直線MO與C的準(zhǔn)線交于Q點(diǎn)（其中O為坐標(biāo)原點(diǎn)），P為C準(zhǔn)線上的一個(gè)動(dòng)點(diǎn)，下列選項(xiàng)正確的是（

）A．當(dāng)直線MN垂直x軸時(shí)，弦MN的長(zhǎng)度最短B．SKIPIF1<0為定值SKIPIF1<0C．當(dāng)PM與C的準(zhǔn)線垂直時(shí)，必有SKIPIF1<0D．至少存在兩個(gè)點(diǎn)P，使得SKIPIF1<039．（2023·廣東汕頭·統(tǒng)考三模）橢圓SKIPIF1<0：SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)SKIPIF1<0，SKIPIF1<0分別作兩條平行的射線SKIPIF1<0，SKIPIF1<0交橢圓C于A，B兩點(diǎn)，（A，B均在x軸上方），則（

）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0B．SKIPIF1<0的最小值為3C．當(dāng)SKIPIF1<0時(shí)，四邊形SKIPIF1<0的面積為SKIPIF1<0D．四邊形SKIPIF1<0面積的最大值為340．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）如圖，已知拋物線SKIPIF1<0，過(guò)拋物線焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0自上而下，分別交拋物線與圓SKIPIF1<0于SKIPIF1<0四點(diǎn)，則（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0第三部分能力提升模擬題41．（2024·江西·校聯(lián)考模擬預(yù)測(cè)）加斯帕爾·蒙日（圖1）是18～19世紀(jì)法國(guó)著名的幾何學(xué)家，他在研究圓錐曲線時(shí)發(fā)現(xiàn)：與橢圓相切的兩條垂直切線的交點(diǎn)的軌跡是以橢圓中心為圓心的圓.我們通常把這個(gè)圓稱(chēng)為該橢圓的蒙日?qǐng)A（圖2）.已知橢圓SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0均在SKIPIF1<0的蒙日?qǐng)ASKIPIF1<0上，SKIPIF1<0，SKIPIF1<0分別與SKIPIF1<0相切于SKIPIF1<0，SKIPIF1<0，則下列說(shuō)法正確的是（

）

A．SKIPIF1<0的蒙日?qǐng)A方程是SKIPIF1<0B．設(shè)SKIPIF1<0，則SKIPIF1<0的取值范圍為SKIPIF1<0C．若點(diǎn)SKIPIF1<0在第一象限的角平分線上，則直線SKIPIF1<0的方程為SKIPIF1<0D．若直線SKIPIF1<0過(guò)原點(diǎn)SKIPIF1<0，且與SKIPIF1<0的一個(gè)交點(diǎn)為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<042．（2023·河北張家口·統(tǒng)考三模）已知SKIPIF1<0是圓SKIPIF1<0上不同的兩點(diǎn)，橢圓SKIPIF1<0的右頂點(diǎn)和上頂點(diǎn)分別為SKIPIF1<0，直線SKIPIF1<0分別是圓SKIPIF1<0的兩條切線，SKIPIF1<0為橢圓SKIPIF1<0的離心率.下列選項(xiàng)正確的有（

）A．直線SKIPIF1<0與橢圓SKIPIF1<0相交B．直線SKIPIF1<0與圓SKIPIF1<0相交C．若橢圓SKIPIF1<0的焦距為SKIPIF1<0兩直線的斜率之積為SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0兩直線的斜率之積為SKIPIF1<0，則SKIPIF1<043．（2023·江蘇揚(yáng)州·統(tǒng)考模擬預(yù)測(cè)）圓柱SKIPIF1<0高為1，下底面圓SKIPIF1<0的直徑SKIPIF1<0長(zhǎng)為2，SKIPIF1<0是圓柱SKIPIF1<0的一條母線，點(diǎn)SKIPIF1<0分別在上、下底面內(nèi)（包含邊界），下列說(shuō)法正確的有（

）．A．若SKIPIF1<0，則SKIPIF1<0點(diǎn)的軌跡為圓B．若直線SKIPIF1<0與直線SKIPIF1<0成SKIPIF1<0，則SKIPIF1<0的軌跡是拋物線的一部分C．存在唯一的一組點(diǎn)SKIPIF1<0，使得SKIPIF1<0D．SKIPIF1<0的取值范圍是SKIPIF1<044．（2023·福建福州·福建省福州第一中學(xué)?？既＃佄锞€C：SKIPIF1<0，AB是C的焦點(diǎn)弦（

）A．點(diǎn)P在C的準(zhǔn)線上，則SKIPIF1<0的最小值為0B．以AB為直徑的所有圓中，圓面積的最小值為9πC．若AB的斜率SKIPIF1<0，則△ABO的面積SKIPIF1<0D．存在一個(gè)半徑為SKIPIF1<0的定圓與以AB為直徑的圓都內(nèi)切45．（2023·廣東汕頭·金山中學(xué)校考三模）已知SKIPIF1<0，SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為橢圓上任意一點(diǎn)（不在SKIPIF1<0軸上），SKIPIF1<0外接圓的圓心為SKIPIF1<0，半徑為SKIPIF1<0，SKIPIF1<0內(nèi)切圓的圓心為SKIPIF1<0，半徑為SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則（

）A．SKIPIF1<0最大時(shí)，SKIPIF1<0 B．SKIPIF1<0的最小值為2C．橢圓SKIPIF1<0的離心率等于SKIPIF1<0 D．SKIPIF1<0的取值范圍為SKIPIF1<046．（2023·湖南·校聯(lián)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0在拋物線C：SKIPIF1<0上，過(guò)P作圓SKIPIF1<0的兩條切線，分別交C于A，B兩點(diǎn)，且直線AB的斜率為SKIPIF1<0，若F為C的焦點(diǎn)，SKIPIF1<0為C上的動(dòng)點(diǎn)，N是C的準(zhǔn)線與坐標(biāo)軸的交點(diǎn)，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的最大值是SKIPIF1<0 D．SKIPIF1<0的最大值是SKIPIF1<047．（2023·山東泰安·統(tǒng)考模擬預(yù)測(cè)）已知拋物線SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，準(zhǔn)線與SKIPIF1<0軸交于SKIPIF1<0點(diǎn)，過(guò)點(diǎn)SKIPIF1<0作不垂直于SKIPIF1<0軸的直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．設(shè)SKIPIF1<0為SKIPIF1<0軸上一動(dòng)點(diǎn)，SKIPIF1<0為SKIPIF1<0的中點(diǎn)，且SKIPIF1<0，則（

）A．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0的斜率為SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．若正三角形SKIPIF1<0的三個(gè)頂點(diǎn)都在拋物線上，則SKIPIF1<0的周長(zhǎng)為SKIPIF1<048．（2023·湖南郴州·校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0，SKIPIF1<0分別為雙曲線SKIPIF1<0：SKIPIF1<0的左?右焦點(diǎn)，SKIPIF1<0為雙曲線SKIPIF1<0的漸近線在第一象限部分上的一點(diǎn)，線段SKIPIF1<0與雙曲線交點(diǎn)為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則下列結(jié)論正確的是（

）A．SKIPIF1<0B．雙曲線SKIPIF1<0的離心率SKIPIF1<0C．SKIPIF1<0D．若SKIPIF1<0的內(nèi)心的橫坐標(biāo)為3，則雙曲線SKIPIF1<0的方程為SKIPIF1<049．（2023·河北滄州·滄縣中學(xué)?？寄M預(yù)測(cè)）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，離心率為SKIPIF1<0，焦點(diǎn)到漸近線的距離為SKIPIF1<0.過(guò)SKIPIF1<0作直線SKIPIF1<0交雙曲線SKIPIF1<0的右支于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0、SKIPIF1<0分別為SKIPIF1<0與SKIPIF1<0的內(nèi)心，則（

）A．SKIPIF1<0的漸近線方程為SKIPIF1<0B．點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0均在同一條定直線上C．直線SKIPIF1<0不可能與SKIPIF1<0平行D．SKIPIF1<0的取值范圍為SKIPIF1<050．（2023·安徽合肥·合肥市第八中學(xué)?？寄M預(yù)測(cè)）如圖，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0分別為雙曲線SKIPIF1<0的左?右焦點(diǎn)，過(guò)雙曲線SKIPIF1<0右支上一點(diǎn)SKIPIF1<0作雙曲線的切線SKIPIF1<0分別交兩漸近線于SKIPIF1<0兩點(diǎn)，交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．若存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，且SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為2或SKIPIF1<051．（2023·廣東·統(tǒng)考模擬預(yù)測(cè)）已知橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作不與坐標(biāo)軸垂直的直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0，SKIPIF1<0在SKIPIF1<0軸上，其中SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），SKIPIF1<0，點(diǎn)SKIPIF1<0為直線SKIPIF1<0，SKIPIF1<0的交點(diǎn)，當(dāng)點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0的上頂點(diǎn)時(shí)，直線SKIPIF1<0與直線SKIPIF1<0垂直，則下列說(shuō)法正確的是（

）A．橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)為SKIPIF1<0B．若點(diǎn)SKIPIF1<0，則SKIPIF1<0的最大值為SKIPIF1<0C．點(diǎn)SKIPIF1<0的橫坐標(biāo)為SKIPIF1<0D．當(dāng)SKIPIF1<0的面積取得最大值時(shí)，直線SKIPIF1<0的斜率為SKIPIF1<052．（2023·山東·校聯(lián)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，若過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0交圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，SKIPIF1<0是圓SKIPIF1<0上的動(dòng)點(diǎn)，則（

）A．SKIPIF1<0的最小值為2B．SKIPIF1<0的最大值為SKIPIF1<0C．SKIPIF1<0的最小值為SKIPIF1<0D．當(dāng)SKIPIF1<0取最大值時(shí)，底邊SKIPIF1<0上的高所在的直線方程為SKIPIF1<053．（2023·廣東深圳·深圳中學(xué)校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0上兩個(gè)不同點(diǎn)，且滿(mǎn)足SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0的最大值為SKIPIF1<0B．SKIPIF1<0的最小值為SKIPIF1<0C．SKIPIF1<0的最大值為SKIPIF1<0D．SKIPIF1<0的最小值為SKIPIF1<054．（2023·山東·沂水縣第一中學(xué)校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0，SKIPIF1<0是經(jīng)過(guò)拋物線SKIPIF1<0焦點(diǎn)SKIPIF1<0的互相垂直的兩條弦，若SKIPIF1<0的傾斜角為銳角，SKIPIF1<0，SKIPIF1<0兩點(diǎn)在SKIPIF1<0軸上方，則下列結(jié)論中一定成立的是（

）A．SKIPIF1<0最小值為32B．設(shè)SKIPIF1<0為拋物線上任意一點(diǎn)，則SKIPIF1<0的最小值為SKIPIF1<0C．若直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0D．SKIPIF1<055．（2023·湖南岳陽(yáng)·統(tǒng)考模擬預(yù)測(cè)）已知雙曲線SKIPIF1<0與橢圓SKIPIF1<0的焦點(diǎn)相同，雙曲線SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線與雙曲線SKIPIF1<0的右支交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0與SKIPIF1<0軸相交于點(diǎn)SKIPIF1<0，SKIPIF1<0的內(nèi)切圓與邊SKIPIF1<0相切于點(diǎn)SKIPIF1<0.若SKIPIF1<0，則下列說(shuō)法正確的有（

）A．雙曲線SKIPIF1<0的漸近線方程