新高考數(shù)學(xué)一輪復(fù)習(xí)10.3 橢圓（精練）（基礎(chǔ)版）（原卷版）

10.3橢圓（精練）（基礎(chǔ)版）題組一題組一橢圓的定義及應(yīng)用1．（2022江西月考）已知SKIPIF1<0是橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0，SKIPIF1<0為橢圓的左，右焦點(diǎn)，且SKIPIF1<0，則SKIPIF1<0()A．1 B．3 C．5 D．92．（2022·江西模擬）“SKIPIF1<0”是“方程SKIPIF1<0表示橢圓”的（）A．充分不必要條件 B．必要不充分雜件C．充要雜件 D．既不充分也不必要條件3．（2022奉賢期中）已知橢圓SKIPIF1<0則（）A．C1與C2頂點(diǎn)相同 B．C1與C2長(zhǎng)軸長(zhǎng)相同C．C1與C2短軸長(zhǎng)相同 D．C1與C2焦距相等4．（2022·南充模擬）已知橢圓SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0相交于不同的兩點(diǎn)SKIPIF1<0，若SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0的斜率為SKIPIF1<0，則橢圓SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·寶雞模擬）“SKIPIF1<0”是“方程SKIPIF1<0表示焦點(diǎn)在x軸上橢圓”的（）A．充要條件 B．充分不必要條件C．必要不充分條件 D．既不充分也不必要條件6．（2022·佛山模擬）若橢圓SKIPIF1<0的焦點(diǎn)在y軸上，則實(shí)數(shù)k的取值范圍是.7．（2022·鄭州模擬）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為F1，F(xiàn)2，O為坐標(biāo)原點(diǎn)，橢圓上一點(diǎn)P滿足|OP|＝3，則△F1PF2的面積為．8．（2022·株洲模擬）已知SKIPIF1<0、SKIPIF1<0是橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，M為橢圓上一點(diǎn)，若SKIPIF1<0為直角三角形，則SKIPIF1<0．9．（2022·奉賢模擬）已知曲線SKIPIF1<0的焦距是10，曲線上的點(diǎn)SKIPIF1<0到一個(gè)焦點(diǎn)的距離是2，則點(diǎn)SKIPIF1<0到另一個(gè)焦點(diǎn)的距離為.10．（202·深圳月考）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0上的一點(diǎn)，且SKIPIF1<0，則SKIPIF1<0面積為．11（2021商丘）設(shè)SKIPIF1<0為橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，P，Q為C上關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的兩點(diǎn)，且SKIPIF1<0，則四邊形SKIPIF1<0的面積為.題組二題組二橢圓的離心率1．（2022·眉山模擬）已知SKIPIF1<0，SKIPIF1<0分別是橢圓SKIPIF1<0的左頂點(diǎn)和右焦點(diǎn)，SKIPIF1<0是橢圓上一點(diǎn)，直線SKIPIF1<0與直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0.且SKIPIF1<0是頂角為120°的等腰三角形，則該橢圓的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·貴州貴陽）設(shè)SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為直線SKIPIF1<0上一點(diǎn)，SKIPIF1<0是底角為SKIPIF1<0的等腰三角形，則橢圓SKIPIF1<0的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·陜西咸陽市）已知橢圓SKIPIF1<0為C的左?右焦點(diǎn)，SKIPIF1<0為C上一點(diǎn)，且SKIPIF1<0的內(nèi)心SKIPIF1<0，若SKIPIF1<0的面積為2b，則n的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．34．（2021·樂清市知臨中學(xué)高三月考）已知橢圓和雙曲線有相同的焦點(diǎn)SKIPIF1<0，它們的離心率分別為SKIPIF1<0，SKIPIF1<0是它們的一個(gè)公共點(diǎn)，且SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2021·江西新余·高三（理））已知SKIPIF1<0是橢圓SKIPIF1<0的左焦點(diǎn)，橢圓SKIPIF1<0上一點(diǎn)SKIPIF1<0關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為SKIPIF1<0，若SKIPIF1<0的周長(zhǎng)為SKIPIF1<0．則離心率SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06（2022·廣東）已知橢圓SKIPIF1<0的左焦點(diǎn)為F，過點(diǎn)F且傾斜角為45°的直線l與橢圓交于A，B兩點(diǎn)（點(diǎn)B在x軸上方），且SKIPIF1<0，則橢圓的離心率為___________.題組三題組三橢圓的標(biāo)準(zhǔn)方程1．（2022湖北月考）已知橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)分別為SKIPIF1<0，P是橢圓上一點(diǎn)，SKIPIF1<0，且C的短半軸長(zhǎng)等于焦距，則橢圓C的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·昌吉期中）已知橢圓過點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0，則此橢圓的方程是（）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．以上均不正確3．（2022福州期中）方程SKIPIF1<0化簡(jiǎn)的結(jié)果是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·寧德期中）已知焦點(diǎn)在SKIPIF1<0軸上的橢圓的離心率為SKIPIF1<0，它的長(zhǎng)軸長(zhǎng)等于圓SKIPIF1<0：SKIPIF1<0的直徑，則橢圓的標(biāo)準(zhǔn)方程是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·溫州期中）已知橢圓一個(gè)焦點(diǎn)SKIPIF1<0，離心率為SKIPIF1<0，則橢圓的標(biāo)準(zhǔn)方程（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022朝陽期中）若橢圓SKIPIF1<0的一個(gè)焦點(diǎn)為SKIPIF1<0，則m的值為（）A．4 B．3 C．2 D．17．（2022·浙江月考）阿基米德是古希臘著名的數(shù)學(xué)家，物理學(xué)家，他利用“逼近法”得到橢圓的面積除以圓周率SKIPIF1<0等于橢圓的長(zhǎng)半軸長(zhǎng)與短半軸長(zhǎng)的乘積.已知在平面直角坐標(biāo)系SKIPIF1<0中，橢圓SKIPIF1<0：SKIPIF1<0的面積為SKIPIF1<0，兩焦點(diǎn)與短軸的一個(gè)端點(diǎn)構(gòu)成等邊三角形，則橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·深圳期中）已知橢圓SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，P是C上一點(diǎn)，SKIPIF1<0垂直于x軸，SKIPIF1<0，則C的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2022江都期中）阿基米德是古希臘著名的數(shù)學(xué)家?物理學(xué)家，他利用“逼近法”得到橢圓的面積除以圓周率SKIPIF1<0等于橢圓的長(zhǎng)半軸長(zhǎng)與短半軸長(zhǎng)的乘積.已知在平面直角坐標(biāo)系SKIPIF1<0中，橢圓SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0的面積為SKIPIF1<0，兩焦點(diǎn)與短軸的一個(gè)端點(diǎn)構(gòu)成等邊三角形，則橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022沈陽期中）阿基米德不僅是著名的物理學(xué)家，也是著名的數(shù)學(xué)家，他利用“逼近法”得到橢圓的面積公式，設(shè)橢圓的長(zhǎng)半軸長(zhǎng)、短半軸長(zhǎng)分別為SKIPIF1<0，則橢圓的面積公式為SKIPIF1<0，若橢圓的離心率為SKIPIF1<0，面積為SKIPIF1<0，則橢圓的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<011．（2022·攀枝花月考）已知橢圓的對(duì)稱中心為坐標(biāo)原點(diǎn)SKIPIF1<0，一個(gè)焦點(diǎn)為直線SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)，離心率為SKIPIF1<0，則橢圓的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．（2022·長(zhǎng)安月考）已知橢圓C的焦點(diǎn)為SKIPIF1<0，過F2的直線與C交于A，B兩點(diǎn).若SKIPIF1<0，SKIPIF1<0，則C的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013（2022西青期末）已知直線SKIPIF1<0經(jīng)過橢圓SKIPIF1<0的左焦點(diǎn)SKIPIF1<0，且與橢圓在第二象限的交點(diǎn)為M，與SKIPIF1<0軸的交點(diǎn)為N，SKIPIF1<0是橢圓的右焦點(diǎn)，且SKIPIF1<0，則橢圓的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題組四題組四直線與橢圓的位置關(guān)系1．（2022云南）直線y＝x＋1與橢圓x2＋SKIPIF1<0＝1的位置關(guān)系是（）A．相離 B．相切 C．相交 D．無法確定2．（2022黑龍江）若直線SKIPIF1<0和圓SKIPIF1<0沒有交點(diǎn)，則過點(diǎn)SKIPIF1<0的直線與橢圓SKIPIF1<0的交點(diǎn)個(gè)數(shù)為（）A．2個(gè) B．至少一個(gè) C．1個(gè) D．0個(gè)3．（2022·江西）已知直線SKIPIF1<0與橢圓SKIPIF1<0恒有公共點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0且SKIPIF1<0 D．SKIPIF1<0且SKIPIF1<04．（2022江蘇）已知以SKIPIF1<0，SKIPIF1<0為焦點(diǎn)的橢圓與直線SKIPIF1<0有且僅有一個(gè)交點(diǎn)，則橢圓的長(zhǎng)軸長(zhǎng)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05（2021·全國(guó)高三專題練習(xí)）已知直線SKIPIF1<0與橢圓SKIPIF1<0相交于與A，B兩點(diǎn)，若橢圓上存在點(diǎn)C，使得SKIPIF1<0，則點(diǎn)C的坐標(biāo)為______________.題組五題組五弦長(zhǎng)1．（2022上海）橢圓SKIPIF1<0中，以點(diǎn)SKIPIF1<0為中點(diǎn)的弦所在直線的斜率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·北京）直線SKIPIF1<0與橢圓SKIPIF1<0相交SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0是橢圓上的動(dòng)點(diǎn)，則SKIPIF1<0面積的最大值為（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．33．（2022·上海市）已知直線SKIPIF1<0交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則直線SKIPIF1<0的斜率為______.4．（2022·全國(guó)·高三專題練習(xí)）已知橢圓SKIPIF1<0(SKIPIF1<0)與直線SKIPIF1<0交于A、B兩點(diǎn)，SKIPIF1<0，且SKIPIF1<0中點(diǎn)的坐標(biāo)為SKIPIF1<0，則此橢圓的方程為________．5．（2022·江蘇）若橢圓SKIPIF1<0的弦AB被點(diǎn)SKIPIF1<0平分，則AB所在的直線方程為______．6．（2022·河北）已知橢圓SKIPIF1<0的一個(gè)焦點(diǎn)與拋物線SKIPIF1<0的焦點(diǎn)重合，過點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線交橢圓SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則橢圓SKIPIF1<0的方程為__．7．（2021·黑龍江）已知橢圓SKIPIF1<0，過SKIPIF1<0點(diǎn)作直線SKIPIF1<0交橢圓SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且點(diǎn)SKIPIF1<0是SKIPIF1<0的中點(diǎn)，則直線SKIPIF1<0的方程是___________.8．（2022·貴州貴陽）已知橢圓SKIPIF1<0的離心率是SKIPIF1<0，點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0