新高考數(shù)學(xué)一輪復(fù)習(xí) 圓錐曲線專項(xiàng)重難點(diǎn)突破專題03 橢圓中的最值問題(原卷版)

專題03橢圓中的最值問題限時(shí)：120分鐘滿分：150分一、單選題：本大題共8小題，每個(gè)小題5分，共40分.在每小題給出的選項(xiàng)中，只有一項(xiàng)是符合題目要求的.1．已知點(diǎn)P為橢圓SKIPIF1<0上任意一點(diǎn)，點(diǎn)M、N分別為SKIPIF1<0和SKIPIF1<0上的點(diǎn)，則SKIPIF1<0的最大值為（

）A．4 B．5 C．6 D．72．點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0上任意一點(diǎn)，SKIPIF1<0分別為左、右焦點(diǎn)，則SKIPIF1<0的最大值為（

）A．2 B．3 C．4 D．不存在3．已知橢圓C：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，圓SKIPIF1<0：SKIPIF1<0，點(diǎn)P和點(diǎn)B分別為橢圓C和圓A上的動(dòng)點(diǎn)，當(dāng)SKIPIF1<0取最小值3時(shí)，SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<04．設(shè)SKIPIF1<0、SKIPIF1<0是橢圓SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)P是直線SKIPIF1<0上一點(diǎn)，則SKIPIF1<0的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知橢圓SKIPIF1<0.過(guò)點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線SKIPIF1<0交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn).將SKIPIF1<0表示為SKIPIF1<0的函數(shù)，則SKIPIF1<0的最大值是（

）A．1 B．2 C．3 D．46．過(guò)橢圓C：SKIPIF1<0上的點(diǎn)SKIPIF1<0，SKIPIF1<0分別作C的切線，若兩切線的交點(diǎn)恰好在直線SKIPIF1<0：SKIPIF1<0上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．－9 D．SKIPIF1<07．已知O為坐標(biāo)原點(diǎn)，橢圓SKIPIF1<0上兩點(diǎn)A，B滿足SKIPIF1<0．若橢圓C上一點(diǎn)M滿足SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．28．已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．8 C．SKIPIF1<0 D．SKIPIF1<0二、多選題：本大題共4小題，每個(gè)小題5分，共20分.在每小題給出的選項(xiàng)中，只有一項(xiàng)或者多項(xiàng)是符合題目要求的.9．已知點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0且SKIPIF1<0，則|PQ|最小時(shí)，m的值可能是（

）A．-1 B．SKIPIF1<0 C．a(chǎn) D．3a10．已知F為橢圓SKIPIF1<0的左焦點(diǎn)．設(shè)P是橢圓C的右準(zhǔn)線上一點(diǎn)，過(guò)點(diǎn)P作橢圓O的兩條切線SKIPIF1<0，切點(diǎn)分別為A，B，則（

）A．SKIPIF1<0的最小值為SKIPIF1<0 B．SKIPIF1<0的最小值為1C．SKIPIF1<0的面積為定值 D．SKIPIF1<0的周長(zhǎng)為定值11．已知SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為橢圓上的動(dòng)點(diǎn)，則下面四個(gè)結(jié)論正確的是（

）A．橢圓的離心率為SKIPIF1<0 B．SKIPIF1<0的最大值為4C．SKIPIF1<0的最大值為3 D．SKIPIF1<0的最大值為SKIPIF1<012．已知F，SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，A，B是橢圓C上關(guān)于原點(diǎn)對(duì)稱的兩點(diǎn)，且已知A，B不是橢圓的頂點(diǎn)，過(guò)點(diǎn)A作SKIPIF1<0軸，垂足為E，直線BE與橢圓C的另一個(gè)交點(diǎn)為P，則（

）A．四邊形SKIPIF1<0的周長(zhǎng)為16 B．SKIPIF1<0的最小值為SKIPIF1<0C．SKIPIF1<0面積的最大值為SKIPIF1<0 D．SKIPIF1<0三、填空題：本大題共4小題，每小題5分，共20分.把答案填在答題卡中的橫線上.13．已知橢圓SKIPIF1<0內(nèi)有一點(diǎn)SKIPIF1<0為橢圓的右焦點(diǎn)，橢圓上有一點(diǎn)SKIPIF1<0，則SKIPIF1<0的最大值為．14．已知SKIPIF1<0為橢圓SKIPIF1<0上一動(dòng)點(diǎn)，點(diǎn)R滿足SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的最大值是．15．已知橢圓SKIPIF1<0（SKIPIF1<0且為常數(shù)）的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上的一點(diǎn)，若SKIPIF1<0的最大值為25，則橢圓SKIPIF1<0的離心率為．16．橢圓SKIPIF1<0上三點(diǎn)A，B，C，其中A位于第一象限，且A，B關(guān)于原點(diǎn)對(duì)稱，C為橢圓右頂點(diǎn)．過(guò)A作x軸的垂線，交直線SKIPIF1<0于D．當(dāng)A在橢圓上運(yùn)動(dòng)時(shí)，總有SKIPIF1<0，則該橢圓離心率e的最大值為．四、解答題：本大題共6小題，共70分.解答應(yīng)寫出必要的文字說(shuō)明、證明過(guò)程或演算步驟．17．已知橢圓M：SKIPIF1<0的一個(gè)焦點(diǎn)為SKIPIF1<0，左、右頂點(diǎn)分別為A，B，經(jīng)過(guò)點(diǎn)F的直線SKIPIF1<0與橢圓M交于C，D兩點(diǎn)．(1)當(dāng)直線SKIPIF1<0的斜率為1時(shí)，求線段CD的長(zhǎng)；(2)記SKIPIF1<0與SKIPIF1<0的面積分別為SKIPIF1<0和SKIPIF1<0，求SKIPIF1<0的最大值．18．已知橢圓SKIPIF1<0過(guò)SKIPIF1<0和SKIPIF1<0兩點(diǎn)．

(1)求橢圓C的方程；(2)如圖所示，記橢圓的左，右頂點(diǎn)分別為A，B，當(dāng)動(dòng)點(diǎn)M在定直線SKIPIF1<0上運(yùn)動(dòng)時(shí)，直線AM，BM分別交橢圓于兩點(diǎn)P和Q，求四邊形SKIPIF1<0面積的最大值．19．已知橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)為4，上頂點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0．(1)求SKIPIF1<0的方程；(2)直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0，SKIPIF1<0分別交直線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求SKIPIF1<0的最小值．20．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，直線SKIPIF1<0與E交于A，B兩點(diǎn)，當(dāng)SKIPIF1<0為雙曲線SKIPIF1<0的一條漸近線時(shí)，A到y(tǒng)軸的距離為SKIPIF1<0.(1)求E的方程；(2)若過(guò)B作x軸的垂線，垂足為H，OH的中點(diǎn)為N（O為坐標(biāo)原點(diǎn)），連接AN并延長(zhǎng)交E于點(diǎn)P，直線PB的斜率為SKIPIF1<0，求SKIPIF1<0的最小值.21．已知橢圓SKIPIF1<0的左頂點(diǎn)為SKIPIF1<0，橢圓SKIPIF1<0的中心SKIPIF1<0關(guān)于直線SKIPIF1<0的對(duì)稱點(diǎn)落在直線SKIPIF1<0上，且橢圓SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0.(1)求橢圓SKIPIF1<0的方程；(2)SKIPIF1<0為橢圓SKIPIF1<0上兩個(gè)動(dòng)點(diǎn)，且直線SKIPIF1<0