新高考數(shù)學(xué)二輪復(fù)習(xí)講練專題17 圓錐曲線常考?jí)狠S小題全歸類（16大題型）（練習(xí)）（原卷版）

專題17圓錐曲線?？?jí)狠S小題全歸類目錄01阿波羅尼斯圓與圓錐曲線 202蒙日?qǐng)A 303阿基米德三角形 304仿射變換問題 405圓錐曲線第二定義 506焦半徑問題 507圓錐曲線第三定義 608定比點(diǎn)差法與點(diǎn)差法 609切線問題 710焦點(diǎn)三角形問題 811焦點(diǎn)弦問題 812圓錐曲線與張角問題 913圓錐曲線與角平分線問題 914圓錐曲線與通徑問題 1015圓錐曲線的光學(xué)性質(zhì)問題 1016圓錐曲線與四心問題 1101阿波羅尼斯圓與圓錐曲線1．（2024·江西贛州·統(tǒng)考模擬預(yù)測(cè)）阿波羅尼斯是古希臘著名數(shù)學(xué)家，與歐幾里得、阿基米德并稱為亞歷山大時(shí)期數(shù)學(xué)三巨匠，他對(duì)圓錐曲線有深刻而系統(tǒng)的研究，阿波羅尼斯圓是他的研究成果之一，指的是：已知?jiǎng)狱c(diǎn)M與兩定點(diǎn)A，B的距離之比為SKIPIF1<0，那么點(diǎn)M的軌跡就是阿波羅尼斯圓，簡(jiǎn)稱阿氏圓．已知在平面直角坐標(biāo)系中，圓SKIPIF1<0、點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0，M為圓O上的動(dòng)點(diǎn)，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2024·全國(guó)·高三專題練習(xí)）已知平面內(nèi)兩個(gè)定點(diǎn)SKIPIF1<0，SKIPIF1<0及動(dòng)點(diǎn)SKIPIF1<0，若SKIPIF1<0（SKIPIF1<0且SKIPIF1<0），則點(diǎn)SKIPIF1<0的軌跡是圓.后世把這種圓稱為阿波羅尼斯圓.已知SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0，直線SKIPIF1<0，若SKIPIF1<0為SKIPIF1<0，SKIPIF1<0的交點(diǎn)，則SKIPIF1<0的最小值為（

）A．3SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2024·全國(guó)·校聯(lián)考模擬預(yù)測(cè)）阿波羅尼斯是古希臘著名數(shù)學(xué)家，與歐幾里得?阿基米德被稱為亞歷山大時(shí)期數(shù)學(xué)三巨匠，阿波羅尼斯發(fā)現(xiàn)：平面內(nèi)到兩個(gè)定點(diǎn)SKIPIF1<0的距離之比為定值SKIPIF1<0，且SKIPIF1<0的點(diǎn)的軌跡是圓，此圓被稱為“阿波羅尼斯圓”.在平面直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0.設(shè)點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0，則下列說法錯(cuò)誤的是（

）A．SKIPIF1<0的方程為SKIPIF1<0B．當(dāng)SKIPIF1<0三點(diǎn)不共線時(shí)，則SKIPIF1<0C．在C上存在點(diǎn)M，使得SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<002蒙日?qǐng)A4．（2024·青海西寧·統(tǒng)考）法國(guó)數(shù)學(xué)家加斯帕·蒙日被稱為“畫法幾何創(chuàng)始人”“微分幾何之父”．他發(fā)現(xiàn)與橢圓相切的兩條互相垂直的切線的交點(diǎn)的軌跡是以該橢圓中心為圓心的圓，這個(gè)圓被稱為該橢圓的蒙日?qǐng)A．若橢圓：SKIPIF1<0（SKIPIF1<0）的蒙日?qǐng)A為SKIPIF1<0，則橢圓Γ的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2024·陜西西安·長(zhǎng)安一中?？迹懊扇?qǐng)A”涉及幾何學(xué)中的一個(gè)著名定理，該定理的內(nèi)容為：橢圓上兩條互相輸出垂直的切線的交點(diǎn)必在一個(gè)與橢圓同心的圓上，該圓稱為橢圓的蒙日?qǐng)A．若橢圓C：SKIPIF1<0的離心率為SKIPIF1<0，則橢圓C的蒙日?qǐng)A的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2024·江西·統(tǒng)考模擬預(yù)測(cè)）定義：圓錐曲線SKIPIF1<0的兩條相互垂直的切線的交點(diǎn)SKIPIF1<0的軌跡是以坐標(biāo)原點(diǎn)為圓心，SKIPIF1<0為半徑的圓，這個(gè)圓稱為蒙日?qǐng)A.已知橢圓SKIPIF1<0的方程為SKIPIF1<0，SKIPIF1<0是直線SKIPIF1<0上的一點(diǎn)，過點(diǎn)SKIPIF1<0作橢圓SKIPIF1<0的兩條切線與橢圓相切于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0是坐標(biāo)原點(diǎn)，連接SKIPIF1<0，當(dāng)SKIPIF1<0為直角時(shí)，則SKIPIF1<0（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<003阿基米德三角形7．（2024·陜西銅川·統(tǒng)考）古希臘哲學(xué)家、百科式科學(xué)家阿基米德最早采用分割法求得橢圓的面積為橢圓的長(zhǎng)半軸長(zhǎng)和短半軸長(zhǎng)乘積的SKIPIF1<0倍，這種方法已具有積分計(jì)算的雛形.已知橢圓SKIPIF1<0的面積為SKIPIF1<0，離心率為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為橢圓SKIPIF1<0上的動(dòng)點(diǎn)，則下列結(jié)論正確的是（

）①橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程可以為SKIPIF1<0

②若SKIPIF1<0，則SKIPIF1<0③存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0

④SKIPIF1<0的最小值為SKIPIF1<0A．①③ B．②④ C．②③ D．①④8．（2024·河北·校聯(lián)考）拋物線的弦與過弦的端點(diǎn)的兩條切線所圍成的三角形稱為阿基米德三角形，在數(shù)學(xué)發(fā)展的歷史長(zhǎng)河中，它不斷地閃煉出真理的光輝，這個(gè)兩千多年的古老圖形，蘊(yùn)藏著很多性質(zhì)．已知拋物線SKIPIF1<0，過焦點(diǎn)的弦SKIPIF1<0的兩個(gè)端點(diǎn)的切線相交于點(diǎn)SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0點(diǎn)必在直線SKIPIF1<0上，且以SKIPIF1<0為直徑的圓過SKIPIF1<0點(diǎn)B．SKIPIF1<0點(diǎn)必在直線SKIPIF1<0上，但以SKIPIF1<0為直徑的圓不過SKIPIF1<0點(diǎn)C．SKIPIF1<0點(diǎn)必在直線SKIPIF1<0上，但以SKIPIF1<0為直徑的圓不過SKIPIF1<0點(diǎn)D．SKIPIF1<0點(diǎn)必在直線SKIPIF1<0上，且以SKIPIF1<0為直徑的圓過SKIPIF1<0點(diǎn)9．（2024·青海西寧·統(tǒng)考）拋物線的弦與過弦的端點(diǎn)的兩條切線所圍成的三角形常被稱為阿基米德三角形．阿基米德三角形有一些有趣的性質(zhì)，如：若拋物線的弦過焦點(diǎn)，則過弦的端點(diǎn)的兩條切線的斜率之積為定值．設(shè)拋物線SKIPIF1<0，弦AB過焦點(diǎn)，△ABQ為阿基米德三角形，則△ABQ的面積的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<004仿射變換問題10．（2024·全國(guó)·高三專題練習(xí)）已知橢圓SKIPIF1<0，SKIPIF1<0分別為橢圓左右焦點(diǎn)，過SKIPIF1<0作兩條互相平行的弦，分別與橢圓交于SKIPIF1<0四點(diǎn)，若當(dāng)兩條弦垂直于SKIPIF1<0軸時(shí)，點(diǎn)SKIPIF1<0所形成的平行四邊形面積最大，則橢圓離心率的取值范圍為.11．（2024·江蘇·高二專題練習(xí)）已知橢圓SKIPIF1<0左頂點(diǎn)為SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0上兩動(dòng)點(diǎn)，直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0，直線SKIPIF1<0的斜率分別為SKIPIF1<0且SKIPIF1<0，SKIPIF1<0（SKIPIF1<0是非零實(shí)數(shù)），求SKIPIF1<0.12．（2024·全國(guó)·高三專題練習(xí)）如圖，作斜率為SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0在直線SKIPIF1<0的上方，則△SKIPIF1<0內(nèi)切圓的圓心所在的定直線方程為．05圓錐曲線第二定義13．（2024·四川眉山·?？寄M預(yù)測(cè)）已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0且斜率為SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2024·江蘇南京·高三南京市第一中學(xué)?？奸_學(xué)考試）已知以F為焦點(diǎn)的拋物線SKIPIF1<0上的兩點(diǎn)A，B，滿足SKIPIF1<0，則弦AB的中點(diǎn)到C的準(zhǔn)線的距離的最大值是（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．415．（2024·全國(guó)·高三專題練習(xí)）已知橢圓SKIPIF1<0=1內(nèi)有一點(diǎn)P（1，-1），F(xiàn)為橢圓的右焦點(diǎn)，在橢圓上有一點(diǎn)M，使|MP|+2|MF|取得最小值，則點(diǎn)M坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<016．（2024·山東濟(jì)寧·統(tǒng)考）過拋物線SKIPIF1<0焦點(diǎn)F的直線與該拋物線及其準(zhǔn)線都相交，交點(diǎn)從左到右依次為A，B，C.若SKIPIF1<0，則線段BC的中點(diǎn)到準(zhǔn)線的距離為（

）A．3 B．4 C．5 D．606焦半徑問題17．（2024·安徽·高二統(tǒng)考期末）過拋物線SKIPIF1<0(a>0)的焦點(diǎn)F作一直線交拋物線于P、Q兩點(diǎn)，若線段PF與FQ的長(zhǎng)分別為p、q，則SKIPIF1<0等于（）A．2 B．SKIPIF1<0 C．SKIPIF1<0SKIPIF1<0 D．SKIPIF1<018．（2024·全國(guó)·高三專題練習(xí)）長(zhǎng)為11的線段AB的兩端點(diǎn)都在雙曲線SKIPIF1<0的右支上，則AB中點(diǎn)M的橫坐標(biāo)的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．（2024·全國(guó)·高三專題練習(xí)）拋物線SKIPIF1<0的焦點(diǎn)弦被焦點(diǎn)分成長(zhǎng)是m和n的兩部分，則m與n的關(guān)系是（

）A．m＋n＝mn B．m＋n＝4 C．mn＝4 D．無(wú)法確定20．已知SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，SKIPIF1<0是該拋物線上的兩點(diǎn)，SKIPIF1<0，則線段SKIPIF1<0的中點(diǎn)到SKIPIF1<0軸的距離為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<007圓錐曲線第三定義21．（2024·貴州貴陽(yáng)·高三統(tǒng)考期末）過拋物線SKIPIF1<0的焦點(diǎn)的直線與拋物線交于A，B兩點(diǎn)，若SKIPIF1<0的中點(diǎn)的縱坐標(biāo)為2，則SKIPIF1<0等于（

）A．4 B．6 C．8 D．1022．（2024·河北石家莊·高三石家莊二中校考開學(xué)考試）過橢圓SKIPIF1<0上一點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線，且切線的斜率小于SKIPIF1<0，切點(diǎn)為SKIPIF1<0，交橢圓另一點(diǎn)SKIPIF1<0，若SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則直線SKIPIF1<0的斜率（

）A．為定值SKIPIF1<0 B．為定值SKIPIF1<0 C．為定值SKIPIF1<0 D．隨SKIPIF1<0變化而變化23．（2024·陜西咸陽(yáng)·統(tǒng)考）已知雙曲線SKIPIF1<0上存在兩點(diǎn)SKIPIF1<0，SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，且線段SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<008定比點(diǎn)差法與點(diǎn)差法24．（2024·浙江溫州·高三溫州中學(xué)?？茧A段練習(xí)）如圖，P為橢圓SKIPIF1<0上的一動(dòng)點(diǎn)，過點(diǎn)P作橢圓SKIPIF1<0的兩條切線PA，PB，斜率分別為SKIPIF1<0，SKIPIF1<0.若SKIPIF1<0為定值，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2024·江蘇南京·高二南京市秦淮中學(xué)?？计谀┮阎甭蕿镾KIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0（SKIPIF1<0），那么SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0，或SKIPIF1<026．（2024·河北衡水·高三河北衡水中學(xué)校考階段練習(xí)）已知橢圓SKIPIF1<0內(nèi)有一定點(diǎn)SKIPIF1<0，過點(diǎn)P的兩條直線SKIPIF1<0，SKIPIF1<0分別與橢圓SKIPIF1<0交于A、C和B、D兩點(diǎn)，且滿足SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0變化時(shí)，直線CD的斜率總為SKIPIF1<0，則橢圓SKIPIF1<0的離心率為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<027．（2024·全國(guó)·高三專題練習(xí)）設(shè)SKIPIF1<0、SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)A、SKIPIF1<0在橢圓上，若SKIPIF1<0，則點(diǎn)A的坐標(biāo)是．09切線問題28．（2024·湖南長(zhǎng)沙·高三雅禮中學(xué)?？茧A段練習(xí)）已知O為坐標(biāo)原點(diǎn)，點(diǎn)P在標(biāo)準(zhǔn)單位圓上，過點(diǎn)P作圓C：SKIPIF1<0的切線，切點(diǎn)為Q，則SKIPIF1<0的最小值為．29．（2024·四川綿陽(yáng)·高三四川省綿陽(yáng)南山中學(xué)校考階段練習(xí)）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，直線SKIPIF1<0為：SKIPIF1<0，設(shè)點(diǎn)SKIPIF1<0為SKIPIF1<0上的一個(gè)動(dòng)點(diǎn)，過點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的兩條切線SKIPIF1<0，其中SKIPIF1<0為切點(diǎn)，則SKIPIF1<0的最小值為．30．（2024·山東濰坊·統(tǒng)考模擬預(yù)測(cè)）在平面直角坐標(biāo)系SKIPIF1<0中，拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0上一點(diǎn)SKIPIF1<0（異于原點(diǎn)SKIPIF1<0）作SKIPIF1<0的切線，與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0．31．（2024·全國(guó)·高三專題練習(xí)）過橢圓SKIPIF1<0上一動(dòng)點(diǎn)SKIPIF1<0分別向圓SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0作切線，切點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍為.10焦點(diǎn)三角形問題32．（2024·河北張家口·高二張家口市第四中學(xué)?？茧A段練習(xí)）已知SKIPIF1<0是雙曲線SKIPIF1<0的一個(gè)焦點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0為坐標(biāo)原點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的面積為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<033．（2024·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0在雙曲線SKIPIF1<0上，其左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，三角形SKIPIF1<0的內(nèi)切圓切x軸于點(diǎn)M，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<034．（2024·江西宜春·上高二中?？寄M預(yù)測(cè)）已知雙曲線SKIPIF1<0(SKIPIF1<0)的左?右焦點(diǎn)分別為SKIPIF1<0為雙曲線上的一點(diǎn)，SKIPIF1<0為SKIPIF1<0的內(nèi)心，且SKIPIF1<0，則SKIPIF1<0的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011焦點(diǎn)弦問題35．（2024·四川內(nèi)江·高三威遠(yuǎn)中學(xué)校?？茧A段練習(xí)）橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交橢圓于SKIPIF1<0兩點(diǎn)，交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0是線段SKIPIF1<0的三等分點(diǎn)，SKIPIF1<0的周長(zhǎng)為SKIPIF1<0，則橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<036．（2024·浙江金華·高二浙江金華第一中學(xué)?？计谀┰O(shè)雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)P在雙曲線上，下列說法正確的是（

）A．若SKIPIF1<0為直角三角形，則SKIPIF1<0的周長(zhǎng)是SKIPIF1<0B．若SKIPIF1<0為直角三角形，則SKIPIF1<0的面積是6C．若SKIPIF1<0為銳角三角形，則SKIPIF1<0的取值范圍是SKIPIF1<0D．若SKIPIF1<0為鈍角三角形，則SKIPIF1<0的取值范圍是SKIPIF1<012圓錐曲線與張角問題37．（2024·山東棗莊·統(tǒng)考）設(shè)SKIPIF1<0、SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0的兩個(gè)焦點(diǎn)，若SKIPIF1<0上存在點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<038．（2024·遼寧朝陽(yáng)·高二統(tǒng)考期末）設(shè)SKIPIF1<0分別為橢圓SKIPIF1<0的左?右焦點(diǎn)，點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上異于頂點(diǎn)的兩點(diǎn)，SKIPIF1<0，則SKIPIF1<0，若點(diǎn)SKIPIF1<0還滿足SKIPIF1<0，則SKIPIF1<0的面積為.39．（2024·浙江杭州·高三浙江大學(xué)附屬中學(xué)?？茧A段練習(xí)）已知O為坐標(biāo)原點(diǎn)，橢圓SKIPIF1<0的左、右焦點(diǎn)分別是SKIPIF1<0，過點(diǎn)SKIPIF1<0且斜率為k的直線與圓SKIPIF1<0交于A，B兩點(diǎn)（點(diǎn)B在x軸上方），線段SKIPIF1<0與橢圓交于點(diǎn)M，SKIPIF1<0延長(zhǎng)線與橢圓交于點(diǎn)N，且SKIPIF1<0，則橢圓的離心率為，直線SKIPIF1<0的斜率為．13圓錐曲線與角平分線問題40．（2024·湖北武漢·武漢二中校聯(lián)考模擬預(yù)測(cè)）已知拋物線SKIPIF1<0上橫坐標(biāo)為4的點(diǎn)到拋物線焦點(diǎn)SKIPIF1<0的距離為SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上的點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0的平分線交拋物線SKIPIF1<0于點(diǎn)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0都在SKIPIF1<0軸的上方，則直線SKIPIF1<0的斜率為.41．（2024·重慶萬(wàn)州·統(tǒng)考模擬預(yù)測(cè)）已知雙曲線C：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，P是C在第一象限上的一點(diǎn)，且直線SKIPIF1<0的斜率為SKIPIF1<0，SKIPIF1<0的平分線交x軸于點(diǎn)A，點(diǎn)B滿足SKIPIF1<0，SKIPIF1<0，則雙曲線C的漸近線方程為．42．（2024·黑龍江·黑龍江實(shí)驗(yàn)中學(xué)?？迹┮阎p曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，離心率為SKIPIF1<0，點(diǎn)SKIPIF1<0是雙曲線上的任意一點(diǎn)，滿足SKIPIF1<0，SKIPIF1<0的平分線與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，則SKIPIF1<0分SKIPIF1<0所得的兩個(gè)三角形的面積之比SKIPIF1<0.43．（2024·湖南·高三長(zhǎng)郡中學(xué)校聯(lián)考階段練習(xí)）已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，離心率為SKIPIF1<0，點(diǎn)SKIPIF1<0是橢圓上的任意一點(diǎn)，滿足SKIPIF1<0的平分線與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，則SKIPIF1<0分SKIPIF1<0所得的兩個(gè)三角形的面積之比SKIPIF1<0.44．（2024·全國(guó)·高三專題練習(xí)）已知點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0上異于頂點(diǎn)的動(dòng)點(diǎn)，SKIPIF1<0，SKIPIF1<0分別為橢圓的左、右焦點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0為SKIPIF1<0的中點(diǎn)，SKIPIF1<0的平分線與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，則四邊形SKIPIF1<0的面積的最大值為.14圓錐曲線與通徑問題45．已知直線SKIPIF1<0過拋物線SKIPIF1<0的焦點(diǎn)，且與SKIPIF1<0的對(duì)稱軸垂直，SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為SKIPIF1<0的準(zhǔn)線上一點(diǎn)，則SKIPIF1<0的面積為（）A．18 B．24 C．36 D．4846．以SKIPIF1<0軸為對(duì)稱軸，拋物線通徑的長(zhǎng)為8，頂點(diǎn)在坐標(biāo)原點(diǎn)的拋物線的方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<047．（2024·貴州黔東南·統(tǒng)考）過雙曲線的焦點(diǎn)與雙曲線實(shí)軸垂直的直線被雙曲線截得的線段的長(zhǎng)稱為雙曲線的通徑，其長(zhǎng)等于SKIPIF1<0(SKIPIF1<0、SKIPIF1<0分別為雙曲線的實(shí)半軸長(zhǎng)與虛半軸長(zhǎng)).已知雙曲線SKIPIF1<0（SKIPIF1<0）的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，若點(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0上位于第四象限的任意一點(diǎn)，直線SKIPIF1<0是雙曲線的經(jīng)過第二、四象限的漸近線，SKIPIF1<0于點(diǎn)SKIPIF1<0，且SKIPIF1<0的最小值為3，則雙曲線SKIPIF1<0的通徑為.15圓錐曲線的光學(xué)性質(zhì)問題48．（2024·四川巴中·高三統(tǒng)考開學(xué)考試）拋物線有如下光學(xué)性質(zhì)：過焦點(diǎn)的光線經(jīng)拋物線反射后得到的光線平行于拋物線的對(duì)稱軸；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的焦點(diǎn)為SKIPIF1<0，一條平行于SKIPIF1<0軸的光線從點(diǎn)SKIPIF1<0射出，經(jīng)過拋物線上的點(diǎn)SKIPIF1<0反射后，再經(jīng)拋物線上的另一點(diǎn)SKIPIF1<0射出，則SKIPIF1<0．49．（2024·山東青島·統(tǒng)考）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，過SKIPIF1<0的直線與SKIPIF1<0交于點(diǎn)SKIPIF1<0、SKIPIF1<0，直線SKIPIF1<0為SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線，點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0的對(duì)稱點(diǎn)為SKIPIF1<0.由橢圓的光學(xué)性質(zhì)知，SKIPIF1<0、SKIPIF1<0、SKIPIF1<0三點(diǎn)共線.若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0.50．（2024·安徽六安·高三六安一中?？茧A段練習(xí)）如圖所示，橢圓有這樣的光學(xué)性質(zhì)：從橢圓的一個(gè)焦點(diǎn)出發(fā)的光線，經(jīng)橢圓反射后，反射光線經(jīng)過橢圓的另一個(gè)焦點(diǎn)．已知橢圓SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0,SKIPIF1<0，P為橢圓上不與頂點(diǎn)重合的任一點(diǎn)，I為SKIPIF1<0的內(nèi)心，記直線OP，PI（O為坐標(biāo)原點(diǎn)）的斜率分別為SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則橢圓的離心率為．16圓錐曲線與四心問題51．（2024·海南海口·?？寄M預(yù)測(cè)）已知SKIPIF1<0、SKIPIF1<0是橢圓SKIPIF1<0的左右焦點(diǎn)，點(diǎn)SKIPIF1<0為SKIPIF1<0上一動(dòng)點(diǎn)，且SKIPIF1<0，若SKIPIF1<0為SKIPIF1<0的內(nèi)心，則SKIPIF1<0面積的