新高考數(shù)學(xué)一輪復(fù)習(xí)第8章 第05講 橢圓 精講（學(xué)生版）

第05講橢圓(精講）目錄第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第二部分：課前自我評(píng)估測(cè)試第三部分：典型例題剖析題型一：橢圓定義的應(yīng)用角度1：利用橢圓定義求軌跡方程角度2：利用橢圓定義解決焦點(diǎn)三角形問(wèn)題角度3：利用橢圓定義求最值題型二：橢圓的標(biāo)準(zhǔn)方程題型三：橢圓的簡(jiǎn)單幾何性質(zhì)角度1：橢圓的長(zhǎng)軸、短軸、焦距角度2：求橢圓的離心率角度3：與橢圓幾何性質(zhì)有關(guān)的最值(范圍)問(wèn)題第四部分：高考真題感悟第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶知識(shí)點(diǎn)一：橢圓的定義平面內(nèi)一個(gè)動(dòng)點(diǎn)SKIPIF1<0到兩個(gè)定點(diǎn)SKIPIF1<0、SKIPIF1<0的距離之和等于常數(shù)SKIPIF1<0，這個(gè)動(dòng)點(diǎn)SKIPIF1<0的軌跡叫橢圓.這兩個(gè)定點(diǎn)（SKIPIF1<0,SKIPIF1<0）叫橢圓的焦點(diǎn)，兩焦點(diǎn)的距離（SKIPIF1<0）叫作橢圓的焦距.說(shuō)明：若SKIPIF1<0，SKIPIF1<0的軌跡為線段SKIPIF1<0；若SKIPIF1<0，SKIPIF1<0的軌跡無(wú)圖形定義的集合語(yǔ)言表述集合SKIPIF1<0.知識(shí)點(diǎn)二：橢圓的標(biāo)準(zhǔn)方程和幾何性質(zhì)1、橢圓的標(biāo)準(zhǔn)方程焦點(diǎn)位置焦點(diǎn)在SKIPIF1<0軸上焦點(diǎn)在SKIPIF1<0軸上標(biāo)準(zhǔn)方程SKIPIF1<0（SKIPIF1<0）SKIPIF1<0（SKIPIF1<0）圖象焦點(diǎn)坐標(biāo)SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0SKIPIF1<0的關(guān)系SKIPIF1<0范圍SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0頂點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0軸長(zhǎng)短軸長(zhǎng)＝SKIPIF1<0，長(zhǎng)軸長(zhǎng)＝SKIPIF1<0焦點(diǎn)SKIPIF1<0SKIPIF1<0焦距SKIPIF1<0對(duì)稱性對(duì)稱軸：SKIPIF1<0軸、SKIPIF1<0軸對(duì)稱中心：原點(diǎn)離心率SKIPIF1<0，SKIPIF1<0知識(shí)點(diǎn)三：常用結(jié)論1、與橢圓SKIPIF1<0SKIPIF1<0共焦點(diǎn)的橢圓方程可設(shè)為：SKIPIF1<0SKIPIF1<02、有相同離心率：SKIPIF1<0（SKIPIF1<0，焦點(diǎn)在SKIPIF1<0軸上）或SKIPIF1<0（SKIPIF1<0，焦點(diǎn)在SKIPIF1<0軸上）3、橢圓SKIPIF1<0的圖象中線段的幾何特征（如下圖）：（1）SKIPIF1<0；（2）SKIPIF1<0，SKIPIF1<0，SKIPIF1<0；（3）SKIPIF1<0,SKIPIF1<0，SKIPIF1<0；（4）橢圓通經(jīng)長(zhǎng)=SKIPIF1<0第二部分：課前自我評(píng)估測(cè)試第二部分：課前自我評(píng)估測(cè)試1．（2022·江蘇·高二）P是橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0，SKIPIF1<0是該橢圓的兩個(gè)焦點(diǎn)，且SKIPIF1<0，則SKIPIF1<0（

）A．1 B．3 C．5 D．92．（2022·湖南·周南中學(xué)高二期末）已知橢圓C：SKIPIF1<0的左右焦點(diǎn)分別為F1、F2，過(guò)左焦點(diǎn)F1，作直線交橢圓C于A、B兩點(diǎn)，則三角形ABF2的周長(zhǎng)為（

）A．10 B．15 C．20 D．253．（2022·浙江紹興·模擬預(yù)測(cè)）已知橢圓SKIPIF1<0，則該橢圓的離心率SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·上海靜安·二模）已知橢圓SKIPIF1<0SKIPIF1<0的一個(gè)焦點(diǎn)坐標(biāo)為SKIPIF1<0，則SKIPIF1<0__________.5．（2022·上海黃浦·模擬預(yù)測(cè)）已知橢圓SKIPIF1<0的左焦點(diǎn)為F，若A?B是橢圓上兩動(dòng)點(diǎn)，且SKIPIF1<0垂直于x軸，則SKIPIF1<0周長(zhǎng)的最大值為_(kāi)__________.第三部分：典型例題剖析第三部分：典型例題剖析題型一：橢圓定義的應(yīng)用角度1：利用橢圓定義求軌跡方程典型例題例題1．（2022·全國(guó)·高二課時(shí)練習(xí)）SKIPIF1<0中，SKIPIF1<0為動(dòng)點(diǎn)，SKIPIF1<0，SKIPIF1<0且滿足SKIPIF1<0，則SKIPIF1<0點(diǎn)的軌跡方程為_(kāi)_____．例題2．（2022·全國(guó)·高二專題練習(xí)）方程SKIPIF1<0化簡(jiǎn)的結(jié)果是___________．例題3．（2022·河北·深州長(zhǎng)江中學(xué)高二期末）已知SKIPIF1<0，SKIPIF1<0是圓SKIPIF1<0上一動(dòng)點(diǎn)，線段SKIPIF1<0的垂直平分線交SKIPIF1<0于SKIPIF1<0，則動(dòng)點(diǎn)SKIPIF1<0的軌跡方程為_(kāi)_____________．例題4．（2022·山西·懷仁市第一中學(xué)校高二期中（文））已知兩圓SKIPIF1<0，動(dòng)圓SKIPIF1<0在圓SKIPIF1<0內(nèi)部且和圓SKIPIF1<0相內(nèi)切．和圓SKIPIF1<0相外切，則動(dòng)圓圓心SKIPIF1<0的軌跡方程為_(kāi)________．同類題型歸類練1．（2022·廣東·廣州市第六十五中學(xué)高二期中）已知定圓SKIPIF1<0，動(dòng)圓C滿足與SKIPIF1<0外切且與SKIPIF1<0內(nèi)切，則動(dòng)圓圓心C的軌跡方程為_(kāi)_________.2．（2022·安徽·六安一中高二期中）已知圓SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0，動(dòng)圓SKIPIF1<0同時(shí)與圓SKIPIF1<0外切和圓SKIPIF1<0內(nèi)切，則動(dòng)圓的圓心SKIPIF1<0的軌跡方程為_(kāi)_______．3．（2022·浙江·金華市江南中學(xué)高二期中）已知點(diǎn)SKIPIF1<0是圓SKIPIF1<0：SKIPIF1<0上動(dòng)點(diǎn)，SKIPIF1<0.若線段SKIPIF1<0的中垂線交SKIPIF1<0于點(diǎn)SKIPIF1<0，則點(diǎn)SKIPIF1<0的軌跡方程為_(kāi)___________.4．（2022·全國(guó)·高二課時(shí)練習(xí)）已知三角形ABC的周長(zhǎng)是8，頂點(diǎn)B，C的坐標(biāo)分別為SKIPIF1<0，（1，0），則頂點(diǎn)A的軌跡方程為_(kāi)_______．角度2：利用橢圓定義解決焦點(diǎn)三角形問(wèn)題典型例題例題1．（2022·安徽省亳州市第一中學(xué)高二期末）設(shè)SKIPIF1<0是橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0是橢圓上一點(diǎn)，且SKIPIF1<0.則SKIPIF1<0的面積為（

）A．6 B．SKIPIF1<0 C．8 D．SKIPIF1<0例題2．（2022·全國(guó)·高二專題練習(xí)）已知橢圓SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為橢圓上動(dòng)點(diǎn)，則SKIPIF1<0的值是______；SKIPIF1<0的取值范圍是______．例題3．（2022·青海青海·高二期末（文））已知橢圓的方程為SKIPIF1<0，過(guò)橢圓中心的直線交橢圓于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0是橢圓的右焦點(diǎn)，則SKIPIF1<0的周長(zhǎng)的最小值為_(kāi)_____．同類題型歸類練1．（2022·江蘇·高二）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0在橢圓上，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．(多選）（2022·廣東·仲元中學(xué)高二期中）雙曲線SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)P在C上.若SKIPIF1<0是直角三角形，則SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．23．（2022·重慶八中模擬預(yù)測(cè)）已知SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，直線SKIPIF1<0與橢圓交于P，Q兩點(diǎn)，則SKIPIF1<0的周長(zhǎng)為_(kāi)_____．4（2022·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0分別為橢圓SKIPIF1<0的左右焦點(diǎn)，傾斜角為SKIPIF1<0的直線SKIPIF1<0經(jīng)過(guò)SKIPIF1<0，且與橢圓交于SKIPIF1<0兩點(diǎn)，則△SKIPIF1<0的周長(zhǎng)為_(kāi)__．7．（2022·全國(guó)·高二專題練習(xí)）已知點(diǎn)SKIPIF1<0在焦點(diǎn)為SKIPIF1<0、SKIPIF1<0的橢圓SKIPIF1<0上，若SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_____．角度3：利用橢圓定義求最值典型例題例題1．（2022·四川遂寧·高二期末（理））已知SKIPIF1<0是橢圓SKIPIF1<0的左焦點(diǎn)，SKIPIF1<0為橢圓SKIPIF1<0上任意一點(diǎn)，點(diǎn)SKIPIF1<0坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．3 B．5 C．SKIPIF1<0 D．13例題2．（2022·全國(guó)·高三專題練習(xí)（文））已知點(diǎn)SKIPIF1<0，且SKIPIF1<0是橢圓SKIPIF1<0的左焦點(diǎn)，SKIPIF1<0是橢圓上任意一點(diǎn)，則SKIPIF1<0的最小值是（

）A．6 B．5 C．4 D．3例題3．（2022·全國(guó)·高二專題練習(xí)）設(shè)SKIPIF1<0是橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0、SKIPIF1<0是橢圓的兩個(gè)焦點(diǎn)，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0同類題型歸類練1．（2022·全國(guó)·高二課時(shí)練習(xí)）已知SKIPIF1<0是橢圓SKIPIF1<0的左焦點(diǎn)，P是此橢圓上的動(dòng)點(diǎn)，SKIPIF1<0是一定點(diǎn)，則SKIPIF1<0的最大值為_(kāi)_____．2．（2022·全國(guó)·高二專題練習(xí)）已知點(diǎn)SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0內(nèi)的兩個(gè)點(diǎn)，M是橢圓上的動(dòng)點(diǎn)，則SKIPIF1<0的最大值為_(kāi)_____．題型二：橢圓的標(biāo)準(zhǔn)方程典型例題例題1．（2022·全國(guó)·高二專題練習(xí)）已知定點(diǎn)SKIPIF1<0、SKIPIF1<0和動(dòng)點(diǎn)SKIPIF1<0．(1)再?gòu)臈l件①、條件②這兩個(gè)條件中選擇一個(gè)作為已知，求：動(dòng)點(diǎn)SKIPIF1<0的軌跡及其方程．條件①：SKIPIF1<0條件②：SKIPIF1<0(2)SKIPIF1<0，求：動(dòng)點(diǎn)SKIPIF1<0的軌跡及其方程．例題2．（2022·四川省資中縣球溪高級(jí)中學(xué)高二階段練習(xí)（文））（1）求焦點(diǎn)在SKIPIF1<0軸上，長(zhǎng)軸長(zhǎng)為6，焦距為4的橢圓標(biāo)準(zhǔn)方程；（2）求離心率SKIPIF1<0，焦點(diǎn)在SKIPIF1<0軸，且經(jīng)過(guò)點(diǎn)SKIPIF1<0的雙曲線標(biāo)準(zhǔn)方程.例題3．（2022·四川省資中縣球溪高級(jí)中學(xué)高二階段練習(xí)（理））（1）求焦點(diǎn)在SKIPIF1<0軸上，長(zhǎng)軸長(zhǎng)為6，焦距為4的橢圓標(biāo)準(zhǔn)方程；（2）求離心率SKIPIF1<0，經(jīng)過(guò)點(diǎn)SKIPIF1<0的雙曲線標(biāo)準(zhǔn)方程．同類題型歸類練1．（2022·江蘇·高二）求適合下列條件的橢圓的標(biāo)準(zhǔn)方程：(1)SKIPIF1<0，SKIPIF1<0；(2)經(jīng)過(guò)點(diǎn)SKIPIF1<0，且與橢圓SKIPIF1<0有共同的焦點(diǎn)；(3)經(jīng)過(guò)SKIPIF1<0，SKIPIF1<0兩點(diǎn)．2．（2022·江蘇·高二）求適合下列條件的橢圓的標(biāo)準(zhǔn)方程：(1)長(zhǎng)軸長(zhǎng)為4，短軸長(zhǎng)為2，焦點(diǎn)在y軸上；(2)經(jīng)過(guò)點(diǎn)SKIPIF1<0，SKIPIF1<0；(3)一個(gè)焦點(diǎn)為SKIPIF1<0，一個(gè)頂點(diǎn)為SKIPIF1<0；(4)一個(gè)焦點(diǎn)為SKIPIF1<0，長(zhǎng)軸長(zhǎng)為4；(5)一個(gè)焦點(diǎn)為SKIPIF1<0，離心率為SKIPIF1<0；(6)一個(gè)焦點(diǎn)到長(zhǎng)軸的兩個(gè)端點(diǎn)的距離分別為6，2.題型三：橢圓的簡(jiǎn)單幾何性質(zhì)角度1：橢圓的長(zhǎng)軸、短軸、焦距典型例題例題1．（2022·全國(guó)·高二課時(shí)練習(xí)）橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)為_(kāi)_____．例題2．（2022·全國(guó)·高二課時(shí)練習(xí)）若橢圓SKIPIF1<0與橢圓SKIPIF1<0焦點(diǎn)相同，則實(shí)數(shù)SKIPIF1<0___________.例題3．（2022·河南·新蔡縣第一高級(jí)中學(xué)高二開(kāi)學(xué)考試（文））已知橢圓SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0為橢圓上一動(dòng)點(diǎn)，則SKIPIF1<0的最大值為_(kāi)___.同類題型歸類練1．（2022·全國(guó)·高三專題練習(xí)）已知橢圓的長(zhǎng)軸長(zhǎng)為SKIPIF1<0，短軸長(zhǎng)為SKIPIF1<0，則橢圓上任意一點(diǎn)SKIPIF1<0到橢圓中心SKIPIF1<0的距離的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國(guó)·高三專題練習(xí)（理））已知曲線SKIPIF1<0的焦距為8，則SKIPIF1<0___________.3．（2022·江蘇·高二課時(shí)練習(xí)）求下列橢圓的長(zhǎng)軸長(zhǎng)、短軸長(zhǎng)、離心率、頂點(diǎn)坐標(biāo)和焦點(diǎn)坐標(biāo)：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0．角度2：求橢圓的離心率典型例題例題1．（2022·貴州黔西·高二期末（理））已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，則橢圓SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·江西上饒·高二期末（理））已知SKIPIF1<0是橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·全國(guó)·高二專題練習(xí)）橢圓SKIPIF1<0的兩焦點(diǎn)為SKIPIF1<0，若橢圓SKIPIF1<0上存在點(diǎn)SKIPIF1<0使SKIPIF1<0為等腰直角三角形，則橢圓SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0例題4．（2022·重慶一中高一期末）已知SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0的左，右焦點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0為等腰三角形，且頂角為SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0例題5．（2022·廣東汕尾·高二期末）設(shè)SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則橢圓SKIPIF1<0的離心率SKIPIF1<0_________.同類題型歸類練1．（2022·江蘇·南京市江寧高級(jí)中學(xué)模擬預(yù)測(cè)）已知橢圓SKIPIF1<0與圓SKIPIF1<0，過(guò)橢圓SKIPIF1<0的頂點(diǎn)作圓SKIPIF1<0的兩條切線，若兩切線互相垂直，則橢圓SKIPIF1<0的離心率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國(guó)·高三專題練習(xí)（理））已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，直線SKIPIF1<0與SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)（SKIPIF1<0在第一象限）.若SKIPIF1<0四點(diǎn)共圓，且直線SKIPIF1<0的傾斜角為SKIPIF1<0，則橢圓SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣東汕頭·二模）已知橢圓C的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，直線AB過(guò)SKIPIF1<0與該橢圓交于A，B兩點(diǎn)，當(dāng)SKIPIF1<0為正三角形時(shí)，該橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·內(nèi)蒙古赤峰·高二期末（文））橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線l交橢圓C于A，B兩點(diǎn)，若SKIPIF1<0，SKIPIF1<0，則橢圓C的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國(guó)·模擬預(yù)測(cè)（文））已知橢圓SKIPIF1<0的右焦點(diǎn)為F，直線SKIPIF1<0與C交于A，B兩點(diǎn)，若以SKIPIF1<0為直徑的圓經(jīng)過(guò)點(diǎn)F，則C的離心率為_(kāi)__________.6．（2022·河北張家口·三模）已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，AB是橢圓過(guò)點(diǎn)SKIPIF1<0的弦，點(diǎn)A關(guān)于原點(diǎn)O的對(duì)稱點(diǎn)為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則橢圓的離心率為_(kāi)__________.7．（2022·遼寧·撫順市第二中學(xué)三模）已知SKIPIF1<0分別為橢圓SKIPIF1<0的左，右焦點(diǎn)，直線SKIPIF1<0與橢圓C的一個(gè)交點(diǎn)為M，若SKIPIF1<0，則橢圓的離心率為_(kāi)_________．角度3：與橢圓幾何性質(zhì)有關(guān)的最值(范圍)問(wèn)題典型例題例題1．（2022·四川·成都外國(guó)語(yǔ)學(xué)校高二開(kāi)學(xué)考試（文））已知兩定點(diǎn)SKIPIF1<0和SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0在直線SKIPIF1<0上移動(dòng)，橢圓SKIPIF1<0以SKIPIF1<0，SKIPIF1<0為焦點(diǎn)且經(jīng)過(guò)點(diǎn)SKIPIF1<0，則橢圓SKIPIF1<0的短軸的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·全國(guó)·高三專題練習(xí)）已知點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上的任意一點(diǎn)，過(guò)點(diǎn)SKIPIF1<0作圓SKIPIF1<0：SKIPIF1<0的切線，設(shè)其中一個(gè)切點(diǎn)為SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·全國(guó)·高三開(kāi)學(xué)考試（文））已知SKIPIF1<0是橢圓SKIPIF1<0上的一個(gè)動(dòng)點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題4．（2022·黑龍江·大慶市東風(fēng)中學(xué)高二開(kāi)學(xué)考試）已知焦點(diǎn)在SKIPIF1<0軸上的橢圓SKIPIF1<0，且SKIPIF1<0，2，SKIPIF1<0成等差數(shù)列，SKIPIF1<0分別是橢圓的左焦點(diǎn)和右頂點(diǎn)，SKIPIF1<0是橢圓上任意一點(diǎn)，則SKIPIF1<0的最大值為（

）A．8 B．10 C．12 D．16同類題型歸類練1．（2022·全國(guó)·高三專題練習(xí)）已知點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上運(yùn)動(dòng)，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江蘇徐州·高二期末）已知橢圓SKIPIF1<0的右頂點(diǎn)為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0