新高考數(shù)學(xué)二輪復(fù)習(xí)分層訓(xùn)練專題23 圓錐曲線的綜合問題（定值 最值 范圍 ）（原卷版）

答案第=page11頁，共=sectionpages22頁專題23圓錐曲線的綜合問題（定值最值范圍）【練基礎(chǔ)】單選題1．（2023·廣東廣州·統(tǒng)考一模）已知拋物線SKIPIF1<0的頂點(diǎn)為坐標(biāo)原點(diǎn)SKIPIF1<0，焦點(diǎn)SKIPIF1<0任SKIPIF1<0鈾上，過點(diǎn)SKIPIF1<0的且線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則直線SKIPIF1<0的斜率的取大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．12．（2023·河南鄭州·統(tǒng)考一模）過拋物線SKIPIF1<0的焦點(diǎn)F作直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的值為（

）A．4 B．6 C．8 D．103．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，P為橢圓上一動(dòng)點(diǎn)，SKIPIF1<0關(guān)于直線SKIPIF1<0的對(duì)稱點(diǎn)為M，SKIPIF1<0關(guān)于直線SKIPIF1<0的對(duì)稱點(diǎn)為N，當(dāng)SKIPIF1<0最大時(shí)，則SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·江西上饒·統(tǒng)考一模）雙曲線C：SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0作垂直于x軸的直線交雙曲線于A，B兩點(diǎn)，則SKIPIF1<0的內(nèi)切圓半徑等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．25．（2023·全國·模擬預(yù)測）已知雙曲線C：SKIPIF1<0的離心率為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0分別是C的左、右焦點(diǎn)，經(jīng)過點(diǎn)SKIPIF1<0且垂直于C的一條漸近線的直線l與C交于A，B兩點(diǎn)，若SKIPIF1<0的面積為64，則C的實(shí)軸長為（

）A．6 B．8 C．12 D．166．（2023·陜西安康·統(tǒng)考二模）設(shè)拋物線C：SKIPIF1<0的焦點(diǎn)是F，直線l與拋物線C相交于A，B兩點(diǎn)，且SKIPIF1<0，過弦AB的中點(diǎn)P作SKIPIF1<0的垂線，垂足為Q，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．SKIPIF1<07．（2023·遼寧阜新·校考模擬預(yù)測）若橢圓SKIPIF1<0的左右焦點(diǎn)為SKIPIF1<0、SKIPIF1<0，過SKIPIF1<0和點(diǎn)SKIPIF1<0的直線交橢圓于M、N兩點(diǎn)，若P（0，m）滿足SKIPIF1<0，則m的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023·內(nèi)蒙古·校聯(lián)考模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0作兩條互相垂直的直線SKIPIF1<0，且直線SKIPIF1<0分別與拋物線SKIPIF1<0交于SKIPIF1<0和SKIPIF1<0，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2023·安徽·統(tǒng)考一模）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，連接SKIPIF1<0并延長，與SKIPIF1<0交于點(diǎn)SKIPIF1<0，則（

）A．SKIPIF1<0的準(zhǔn)線方程為SKIPIF1<0 B．點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)C．直線SKIPIF1<0與SKIPIF1<0相切 D．SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與直線SKIPIF1<0平行10．（2023·全國·模擬預(yù)測）已知橢圓SKIPIF1<0：SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0外一點(diǎn)，過點(diǎn)SKIPIF1<0作橢圓SKIPIF1<0的兩條不同的切線SKIPIF1<0，SKIPIF1<0，切點(diǎn)分別為SKIPIF1<0，SKIPIF1<0.已知當(dāng)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)時(shí)，恒有SKIPIF1<0.則（

）A．SKIPIF1<0B．若矩形SKIPIF1<0的四條邊均與橢圓SKIPIF1<0相切，則矩形SKIPIF1<0的面積的最小值為14C．若點(diǎn)SKIPIF1<0的運(yùn)動(dòng)軌跡為SKIPIF1<0，則原點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離恒為1D．若直線SKIPIF1<0，SKIPIF1<0的斜率存在且其斜率之積為SKIPIF1<0，則點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上運(yùn)動(dòng)11．（2023·全國·模擬預(yù)測）已知橢圓SKIPIF1<0（SKIPIF1<0）的離心率為SKIPIF1<0，橢圓上一點(diǎn)P與焦點(diǎn)SKIPIF1<0所形成的三角形面積最大值為SKIPIF1<0，下列說法正確的是（

）A．橢圓方程為SKIPIF1<0B．直線SKIPIF1<0與橢圓C無公共點(diǎn)C．若A，B為橢圓C上的動(dòng)點(diǎn)，且SKIPIF1<0，過SKIPIF1<0作SKIPIF1<0，SKIPIF1<0為垂足，則點(diǎn)H所在軌跡為圓，且圓的半徑SKIPIF1<0滿足SKIPIF1<0D．若過點(diǎn)SKIPIF1<0作橢圓的兩條切線，切點(diǎn)分別為A，B，則SKIPIF1<012．（2023·安徽淮北·統(tǒng)考一模）已知曲線SKIPIF1<0，直線l過點(diǎn)SKIPIF1<0交SKIPIF1<0于A，B兩點(diǎn)，下列命題正確的有（

）A．若A點(diǎn)橫坐標(biāo)為8，則SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0的最小值為6C．原點(diǎn)O在AB上的投影的軌跡與直線SKIPIF1<0有且只有一個(gè)公共點(diǎn)D．若SKIPIF1<0，則以線段AB為直徑的圓的面積是SKIPIF1<0三、填空題13．（2023·福建福州·統(tǒng)考二模）已知橢圓C：SKIPIF1<0，直線l與C在第二象限交于A，B兩點(diǎn)（A在B的左下方），與x軸，y軸分別交于點(diǎn)M，N，且|MA|：|AB|：|BN|=1：2：3，則l的方程為__________．14．（2023·貴州貴陽·統(tǒng)考一模）拋物線SKIPIF1<0，圓SKIPIF1<0，直線l過圓心M且與拋物線E交于A，B與圓M交于C，D.若SKIPIF1<0，則SKIPIF1<0___________.15．（2023·內(nèi)蒙古赤峰·統(tǒng)考模擬預(yù)測）拋物線SKIPIF1<0的焦點(diǎn)為F，過C上一點(diǎn)P作C的準(zhǔn)線l的垂線，垂足為A，若直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0的面積為______．16．（2023·陜西·西安市西光中學(xué)校聯(lián)考一模）點(diǎn)A，B是拋物線C：SKIPIF1<0上的兩點(diǎn)，F(xiàn)是拋物線C的焦點(diǎn)，若SKIPIF1<0，AB中點(diǎn)D到拋物線C的準(zhǔn)線的距離為d，則SKIPIF1<0的最小值為________.四、解答題17．（2023·廣東廣州·統(tǒng)考一模）已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，以C的短軸為直徑的圓與直線SKIPIF1<0相切.(1)求C的方程；(2)直線SKIPIF1<0：SKIPIF1<0與C相交于A，B兩點(diǎn)，過C上的點(diǎn)P作x軸的平行線交線段AB于點(diǎn)Q，直線OP的斜率為SKIPIF1<0（O為坐標(biāo)原點(diǎn)），△APQ的面積為SKIPIF1<0.SKIPIF1<0的面積為SKIPIF1<0，若SKIPIF1<0，判斷SKIPIF1<0是否為定值？并說明理由.18．（2023·山東泰安·統(tǒng)考一模）已知橢圓SKIPIF1<0：SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，離心率為SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0上不同的兩點(diǎn)，且點(diǎn)SKIPIF1<0在SKIPIF1<0軸上方，SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0交于點(diǎn)SKIPIF1<0.已知當(dāng)SKIPIF1<0軸時(shí)，SKIPIF1<0.(1)求橢圓SKIPIF1<0的方程；(2)求證：點(diǎn)SKIPIF1<0在以SKIPIF1<0，SKIPIF1<0為焦點(diǎn)的定橢圓上.【提能力】一、單選題19．（2023·全國·高三專題練習(xí)）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0且斜率大于零的直線SKIPIF1<0與SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若直線SKIPIF1<0與拋物線SKIPIF1<0相切，則SKIPIF1<0（

）A．4 B．6 C．8 D．1020．（2023·全國·模擬預(yù)測）已知拋物線C：SKIPIF1<0，O為坐標(biāo)原點(diǎn)，A，B是拋物線C上兩點(diǎn)，記直線OA，OB的斜率分別為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，直線AB與x軸的交點(diǎn)為P，直線OA、OB與拋物線C的準(zhǔn)線分別交于點(diǎn)M，N，則△PMN的面積的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．（2023·廣西梧州·統(tǒng)考一模）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為雙曲線SKIPIF1<0右支上的動(dòng)點(diǎn)，過SKIPIF1<0作兩漸近線的垂線，垂足分別為SKIPIF1<0，SKIPIF1<0．若圓SKIPIF1<0與雙曲線SKIPIF1<0的漸近線相切，則下列結(jié)論正確的有（

）個(gè)．①SKIPIF1<0；②SKIPIF1<0為定值；③雙曲線SKIPIF1<0的離心率SKIPIF1<0；④當(dāng)點(diǎn)SKIPIF1<0異于頂點(diǎn)時(shí)，△SKIPIF1<0的內(nèi)切圓的圓心總在直線SKIPIF1<0上．A．1 B．2 C．3 D．422．（2023·江西景德鎮(zhèn)·統(tǒng)考模擬預(yù)測）已知雙曲線SKIPIF1<0：SKIPIF1<0的左、右頂點(diǎn)為P、Q，點(diǎn)D在雙曲線上且位于第一象限，若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．（2022·全國·高三專題練習(xí)）已知O為坐標(biāo)原點(diǎn)，焦點(diǎn)在x軸上的曲線C：SKIPIF1<0的離心率SKIPIF1<0滿足SKIPIF1<0，A，B是x軸與曲線C的交點(diǎn)，P是曲線C上異于A，B的一點(diǎn)，延長PO交曲線C于另一點(diǎn)Q，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2022·廣東廣州·統(tǒng)考一模）雙曲線SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，過SKIPIF1<0作垂直于SKIPIF1<0軸的直線交雙曲線于SKIPIF1<0兩點(diǎn)，SKIPIF1<0的內(nèi)切圓圓心分別為SKIPIF1<0，則SKIPIF1<0的面積是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023春·甘肅張掖·高三高臺(tái)縣第一中學(xué)統(tǒng)考期末）橢圓SKIPIF1<0的左?右頂點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上，且直線SKIPIF1<0斜率取值范圍是SKIPIF1<0，那么直線SKIPIF1<0斜率取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<026．（2022·青海西寧·湟川中學(xué)?？家荒＃┮阎獟佄锞€SKIPIF1<0的焦點(diǎn)為F，過點(diǎn)F的直線l與拋物線C在第一、四象限分別交于點(diǎn)A，B，與圓SKIPIF1<0相切，則SKIPIF1<0的值等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題27．（2023·山東臨沂·統(tǒng)考一模）拋物線有如下光學(xué)性質(zhì)：由其焦點(diǎn)射出的光線經(jīng)拋物線反射后，沿平行于拋物線對(duì)稱軸的方向射出．反之，平行于拋物線對(duì)稱軸的入射光線經(jīng)拋物線反射后必過拋物線的焦點(diǎn)．已知拋物線SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，一束平行于SKIPIF1<0軸的光線SKIPIF1<0從點(diǎn)SKIPIF1<0射入，經(jīng)過SKIPIF1<0上的點(diǎn)SKIPIF1<0反射后，再經(jīng)過SKIPIF1<0上另一點(diǎn)SKIPIF1<0反射后，沿直線SKIPIF1<0射出，經(jīng)過點(diǎn)SKIPIF1<0，則（）A．SKIPIF1<0B．延長SKIPIF1<0交直線SKIPIF1<0于點(diǎn)SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三點(diǎn)共線C．SKIPIF1<0D．若SKIPIF1<0平分SKIPIF1<0，則SKIPIF1<028．（2023·浙江·模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線與x軸的交點(diǎn)為M，過點(diǎn)F的直線l與拋物線C相交于A，B兩點(diǎn)（點(diǎn)A在第一象限），過A，B點(diǎn)作準(zhǔn)線的垂線，垂足分別為SKIPIF1<0．設(shè)直線l的傾斜角為SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．則下列說法正確的是（

）A．SKIPIF1<0有可能為直角B．SKIPIF1<0C．Q為拋物線C上一個(gè)動(dòng)點(diǎn)，SKIPIF1<0為定點(diǎn)，SKIPIF1<0的最小值為SKIPIF1<0D．過F點(diǎn)作傾斜角的角平分線FP交拋物線C于P點(diǎn)（點(diǎn)P在第一象限），則存在SKIPIF1<0，使SKIPIF1<029．（2023·全國·開灤第二中學(xué)?？寄M預(yù)測）設(shè)SKIPIF1<0，SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，P為橢圓上第一象限內(nèi)任意一點(diǎn)，SKIPIF1<0，SKIPIF1<0表示直線SKIPIF1<0，SKIPIF1<0的斜率，則下列說法正確的是（

）A．存在點(diǎn)P，使得SKIPIF1<0成立 B．存在點(diǎn)P，使得SKIPIF1<0成立C．存在點(diǎn)P，使得SKIPIF1<0成立 D．存在點(diǎn)P，使得SKIPIF1<0成立30．（2023·山東濟(jì)寧·統(tǒng)考一模）已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0(SKIPIF1<0)與雙曲線SKIPIF1<0：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SKIPIF1<0是SKIPIF1<0與SKIPIF1<0的一個(gè)公共點(diǎn)，滿足SKIPIF1<0，則下列結(jié)論中正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的最大值為SKIPIF1<0 D．SKIPIF1<0的最大值為SKIPIF1<0三、填空題31．（2023·陜西咸陽·陜西咸陽中學(xué)?？寄M預(yù)測）已知拋物線SKIPIF1<0，過焦點(diǎn)的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0在拋物線SKIPIF1<0的準(zhǔn)線上，且滿足SKIPIF1<0，則直線SKIPIF1<0的方程為___________.32．（2023秋·湖南湘潭·高三校聯(lián)考期末）已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，直線SKIPIF1<0與雙曲線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0，以SKIPIF1<0為直徑的圓與SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，則SKIPIF1<0__________.33．（2023·湖北武漢·統(tǒng)考模擬預(yù)測）設(shè)F為雙曲線SKIPIF1<0的右焦點(diǎn)，A，B分別為雙曲線E的左右頂點(diǎn)，點(diǎn)P為雙曲線E上異于A，B的動(dòng)點(diǎn)，直線l：x＝t使得過F作直線AP的垂線交直線l于點(diǎn)Q時(shí)總有B，P，Q三點(diǎn)共線，則SKIPIF1<0的最大值為____________.34．（2023·全國·模擬預(yù)測）已知橢圓SKIPIF1<0，斜率為SKIPIF1<0的直線SKIPIF1<0分別交SKIPIF1<0軸負(fù)半軸、SKIPIF1<0軸負(fù)半軸于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0軸上方，過點(diǎn)SKIPIF1<0作SKIPIF1<0軸的平行線交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，則SKIPIF1<0面積的最大值為____