新高考數(shù)學(xué)二輪復(fù)習(xí)考點(diǎn)講義第二十六講圓錐曲線（原卷版）

第二十六講：橢圓、雙曲線、拋物線【考點(diǎn)梳理】求曲線的軌跡方程直接法、定義法、相關(guān)點(diǎn)法橢圓方程橢圓相關(guān)計(jì)算（1）橢圓標(biāo)準(zhǔn)方程中的三個(gè)量SKIPIF1<0的幾何意義SKIPIF1<0（2）通徑:過焦點(diǎn)且垂直于長(zhǎng)軸的弦,其長(zhǎng)SKIPIF1<0焦點(diǎn)弦：橢圓過焦點(diǎn)的弦。最短的焦點(diǎn)弦為通經(jīng)SKIPIF1<0，最長(zhǎng)為SKIPIF1<0。（3）最大角:SKIPIF1<0是橢圓上一點(diǎn)，當(dāng)SKIPIF1<0是橢圓的短軸端點(diǎn)時(shí)，SKIPIF1<0為最大角。（4）橢圓上一點(diǎn)和兩個(gè)焦點(diǎn)構(gòu)成的三角形稱為焦點(diǎn)三角形。焦點(diǎn)三角形的面積SKIPIF1<0，其中SKIPIF1<0（注意公式的推導(dǎo)）雙曲線（1）雙曲線的通徑過雙曲線的焦點(diǎn)且與雙曲線實(shí)軸垂直的直線被雙曲線截得的線段，稱為雙曲線的通徑．通徑長(zhǎng)為SKIPIF1<0．（2）點(diǎn)與雙曲線的位置關(guān)系對(duì)于雙曲線SKIPIF1<0，點(diǎn)SKIPIF1<0在雙曲線內(nèi)部，等價(jià)于SKIPIF1<0．點(diǎn)SKIPIF1<0在雙曲線外部，等價(jià)于SKIPIF1<0結(jié)合線性規(guī)劃的知識(shí)點(diǎn)來分析．（3）雙曲線?？夹再|(zhì)性質(zhì)1：雙曲線的焦點(diǎn)到兩條漸近線的距離為常數(shù)SKIPIF1<0；頂點(diǎn)到兩條漸近線的距離為常數(shù)SKIPIF1<0;性質(zhì)2：雙曲線上的任意點(diǎn)SKIPIF1<0到雙曲線C的兩條漸近線的距離的乘積是一個(gè)常數(shù)SKIPIF1<0；（4）雙曲線焦點(diǎn)三角形面積為SKIPIF1<0（可以這樣理解，頂點(diǎn)越高，張角越小，分母越小，面積越大）（5）雙曲線的切線點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0SKIPIF1<0上，過點(diǎn)SKIPIF1<0作雙曲線的切線方程為SKIPIF1<0．若點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0SKIPIF1<0外，則點(diǎn)SKIPIF1<0對(duì)應(yīng)切點(diǎn)弦方程為SKIPIF1<0拋物線（1）、焦半徑拋物線上的點(diǎn)SKIPIF1<0與焦點(diǎn)SKIPIF1<0的距離稱為焦半徑，若SKIPIF1<0，則焦半徑SKIPIF1<0，SKIPIF1<0．（2）、焦點(diǎn)弦若SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)弦，SKIPIF1<0，SKIPIF1<0，則有以下結(jié)論：（1）SKIPIF1<0．（2）SKIPIF1<0．（3）焦點(diǎn)弦長(zhǎng)公式1：SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，焦點(diǎn)弦取最小值SKIPIF1<0，即所有焦點(diǎn)弦中通徑最短，其長(zhǎng)度為SKIPIF1<0．焦點(diǎn)弦長(zhǎng)公式2：SKIPIF1<0（SKIPIF1<0為直線SKIPIF1<0與對(duì)稱軸的夾角）．（4）SKIPIF1<0的面積公式：SKIPIF1<0（SKIPIF1<0為直線SKIPIF1<0與對(duì)稱軸的夾角）．（3）、拋物線的通徑過焦點(diǎn)且垂直于拋物線對(duì)稱軸的弦叫做拋物線的通徑．對(duì)于拋物線SKIPIF1<0，由SKIPIF1<0，SKIPIF1<0，可得SKIPIF1<0，故拋物線的通徑長(zhǎng)為SKIPIF1<0．（4）、弦的中點(diǎn)坐標(biāo)與弦所在直線的斜率的關(guān)系：SKIPIF1<0（5）、焦點(diǎn)弦的常考性質(zhì)已知SKIPIF1<0、SKIPIF1<0是過拋物線SKIPIF1<0焦點(diǎn)SKIPIF1<0的弦，SKIPIF1<0是SKIPIF1<0的中點(diǎn)，SKIPIF1<0是拋物線的準(zhǔn)線，SKIPIF1<0，SKIPIF1<0為垂足．（1）以SKIPIF1<0為直徑的圓必與準(zhǔn)線SKIPIF1<0相切，以AF（或BF）為直徑的圓與y軸相切；（2）SKIPIF1<0，SKIPIF1<0（3）SKIPIF1<0；SKIPIF1<0（4）設(shè)SKIPIF1<0，SKIPIF1<0為垂足，則SKIPIF1<0、SKIPIF1<0、SKIPIF1<0三點(diǎn)在一條直線上【典型題型講解】考點(diǎn)一：橢圓【典例例題】例1．（2022·廣東清遠(yuǎn)·高三期末）若橢圓SKIPIF1<0的焦距為6，則實(shí)數(shù)SKIPIF1<0（

）A．13 B．40 C．5 D．SKIPIF1<0例2．（2022·廣東珠海·高三期末）已知橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)為4，左頂點(diǎn)A到上頂點(diǎn)B的距離為SKIPIF1<0，F(xiàn)為右焦點(diǎn)．(1)求橢圓C的方程和離心率；(2)設(shè)直線l與橢圓C交于不同的兩點(diǎn)M，N（不同于A，B兩點(diǎn)），且直線SKIPIF1<0時(shí)，求F在l上的射影H的軌跡方程．【方法技巧與總結(jié)】標(biāo)準(zhǔn)方程SKIPIF1<0SKIPIF1<0圖形性質(zhì)焦點(diǎn)SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0焦距SKIPIF1<0SKIPIF1<0范圍SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0對(duì)稱性關(guān)于SKIPIF1<0軸、SKIPIF1<0軸和原點(diǎn)對(duì)稱頂點(diǎn)SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0軸長(zhǎng)軸長(zhǎng)SKIPIF1<0SKIPIF1<0，短軸長(zhǎng)SKIPIF1<0SKIPIF1<0離心率SKIPIF1<0（注：離心率越小越圓，越大越扁）【變式訓(xùn)練】1．（2022·廣東佛山·高三期末）（多選）已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，上頂點(diǎn)為B，且SKIPIF1<0，點(diǎn)P在C上，線段SKIPIF1<0與SKIPIF1<0交于Q，SKIPIF1<0，則（

）A．橢圓C的離心率為SKIPIF1<0 B．橢圓C上存在點(diǎn)K，使得SKIPIF1<0C．直線SKIPIF1<0的斜率為SKIPIF1<0 D．SKIPIF1<0平分SKIPIF1<02．（2022·廣東·金山中學(xué)高三期末）已知橢圓SKIPIF1<0：SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0，若在橢圓SKIPIF1<0上不存在點(diǎn)P，使得由點(diǎn)P所作的圓SKIPIF1<0的兩條切線互相垂直，則橢圓SKIPIF1<0的離心率的取值范圍是________.3.（2022·廣東汕尾·高三期末）已知SKIPIF1<0分別是橢圓C：SKIPIF1<0的左、右兩個(gè)焦點(diǎn)，若橢圓C上存在四個(gè)不同的點(diǎn)P，使得SKIPIF1<0，的面積為SKIPIF1<0，則正實(shí)數(shù)m的取值范圍為______．4．（2022·廣東肇慶·二模）已知點(diǎn)SKIPIF1<0，SKIPIF1<0分別是橢圓SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)A是橢圓上一點(diǎn)，點(diǎn)О為坐標(biāo)原點(diǎn)，若SKIPIF1<0，直線SKIPIF1<0的斜率為SKIPIF1<0，則橢圓C的離心率為（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（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<06．（2022·廣東中山·高三期末）已知橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0,離心率為SKIPIF1<0,直線SKIPIF1<0被橢圓截得的弦長(zhǎng)為SKIPIF1<0SKIPIF1<0求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程SKIPIF1<0若SKIPIF1<0是橢圓SKIPIF1<0上一點(diǎn),SKIPIF1<0是坐標(biāo)原點(diǎn),過點(diǎn)SKIPIF1<0與直線SKIPIF1<0平行的直線與橢圓SKIPIF1<0的兩個(gè)交點(diǎn)為SKIPIF1<0,且SKIPIF1<0,求SKIPIF1<0的最大值7．（2022·廣東·金山中學(xué)高三期末）在平面直角坐標(biāo)系xOy中，橢圓C：SKIPIF1<0的左，右頂點(diǎn)分別為A、B，點(diǎn)F是橢圓的右焦點(diǎn)，SKIPIF1<0，SKIPIF1<0．(1)求橢圓C的方程；(2)不過點(diǎn)A的直線l交橢圓C于M、N兩點(diǎn)，記直線l、AM、AN的斜率分別為k、SKIPIF1<0、SKIPIF1<0．若SKIPIF1<0，證明直線l過定點(diǎn)，并求出定點(diǎn)的坐標(biāo)．8．（2022·廣東潮州·高三期末）已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，以原點(diǎn)O為圓心，橢圓C的長(zhǎng)半軸長(zhǎng)為半徑的圓與直線SKIPIF1<0相切．(1)求橢圓C的標(biāo)準(zhǔn)方程；(2)已知點(diǎn)A，B為動(dòng)直線y=k(x-2)(k≠0)與橢圓C的兩個(gè)交點(diǎn)，問：在x軸上是否存在定點(diǎn)E，使得SKIPIF1<0為定值？若存在，試求出點(diǎn)E的坐標(biāo)和定值；若不存在，請(qǐng)說明理由．9．（2022·廣東東莞·高三期末）已知點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0的左頂點(diǎn)，點(diǎn)SKIPIF1<0為右焦點(diǎn)，直線SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0，且SKIPIF1<0，點(diǎn)SKIPIF1<0為橢圓上異于點(diǎn)SKIPIF1<0的任意一點(diǎn)，直線SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0.(1)求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)證明：SKIPIF1<0.10．（2022·廣東深圳·高三期末）在平面直角坐標(biāo)系SKIPIF1<0中，點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，過點(diǎn)SKIPIF1<0的直線l與C交于M，N兩點(diǎn)（異于點(diǎn)A），記直線AM，AN的斜率分別為SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．(1)求C的方程；(2)證明：SKIPIF1<0為定值．11．（2021·廣東汕頭·高三期末）已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，又點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上．(1)求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)若動(dòng)直線SKIPIF1<0與橢圓SKIPIF1<0有且只有一個(gè)公共點(diǎn)，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0的垂線，垂足為SKIPIF1<0，試探究：SKIPIF1<0是否為定值，如果是，請(qǐng)求出該值；如果不是，請(qǐng)說明理由.12．（2022·廣東潮州·二模）設(shè)橢圓SKIPIF1<0為左右焦點(diǎn),SKIPIF1<0為短軸端點(diǎn),長(zhǎng)軸長(zhǎng)為4,焦距為SKIPIF1<0,且SKIPIF1<0,SKIPIF1<0的面積為SKIPIF1<0.(Ⅰ)求橢圓SKIPIF1<0的方程(Ⅱ)設(shè)動(dòng)直線SKIPIF1<0橢圓SKIPIF1<0有且僅有一個(gè)公共點(diǎn)SKIPIF1<0,且與直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0.試探究:在坐標(biāo)平面內(nèi)是否存在定點(diǎn)SKIPIF1<0,使得以SKIPIF1<0為直徑的圓恒過點(diǎn)SKIPIF1<0?若存在求出點(diǎn)SKIPIF1<0的坐標(biāo),若不存在.請(qǐng)說明理由.考點(diǎn)二：雙曲線【典例例題】例1．（2022·廣東珠海·高三期末）雙曲線SKIPIF1<0的右支上一點(diǎn)M關(guān)于原點(diǎn)O的對(duì)稱點(diǎn)為點(diǎn)N，F(xiàn)為雙曲線的右焦點(diǎn)，若SKIPIF1<0，SKIPIF1<0，則雙曲線C的離心率e為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例2．（2022·廣東佛山·高三期末）已知雙曲線C的漸近線方程為SKIPIF1<0，且過點(diǎn)SKIPIF1<0.(1)求C的方程；(2)設(shè)SKIPIF1<0，直線SKIPIF1<0不經(jīng)過P點(diǎn)且與C相交于A，B兩點(diǎn)，若直線SKIPIF1<0與C交于另一點(diǎn)D，求證：直線SKIPIF1<0過定點(diǎn).【方法技巧與總結(jié)】1.雙曲線的定義：焦點(diǎn)三角形2.雙曲線的性質(zhì)：離心率、雙曲線的漸近線【變式訓(xùn)練】1．（2022·廣東潮州·高三期末）SKIPIF1<0、SKIPIF1<0分別為雙曲線SKIPIF1<0的左、右焦點(diǎn)，過SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0的左、右兩支曲線分別交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·廣東汕尾·高三期末）已知雙曲線SKIPIF1<0的漸近線方程為SKIPIF1<0，則該雙曲線的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．23．（2022·廣東清遠(yuǎn)·高三期末）（多選）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，點(diǎn)P是雙曲線C上位于第一象限的點(diǎn)，過點(diǎn)SKIPIF1<0作SKIPIF1<0的角平分線的垂線，垂足為A，若O為坐標(biāo)原點(diǎn)，SKIPIF1<0，則（

）A．雙曲線C的漸近線方程為SKIPIF1<0B．雙曲線C的漸近線方程為SKIPIF1<0C．雙曲線C的離心率為SKIPIF1<0D．雙曲線C的離心率為SKIPIF1<04.（2022·廣東東莞·高三期末）已知SKIPIF1<0為雙曲線SKIPIF1<0：SKIPIF1<0的一個(gè)焦點(diǎn)，則點(diǎn)SKIPIF1<0到雙曲線SKIPIF1<0的一條漸近線的距離為_______.5.（2022·廣東深圳·高三期末）在平面直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0為雙曲線SKIPIF1<0的一個(gè)焦點(diǎn)，以SKIPIF1<0為圓心的圓與SKIPIF1<0的兩條漸近線交于SKIPIF1<0、SKIPIF1<0、SKIPIF1<0三點(diǎn)，若四邊形SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0的離心率為______．6.（2022·廣東中山·高三期末）已知點(diǎn)M為雙曲線C：SKIPIF1<0在第一象限上一點(diǎn)，點(diǎn)F為雙曲線C的右焦點(diǎn)，O為坐標(biāo)原點(diǎn)，SKIPIF1<0，則雙曲線C的離心率為___________；若SKIPIF1<0分別交雙曲線C于P、Q兩點(diǎn)，記直線QM與PQ的斜率分別為SKIPIF1<0，則SKIPIF1<0___________．29．（2022·廣東深圳·一模）已知雙曲線SKIPIF1<0：SKIPIF1<0經(jīng)過點(diǎn)ASKIPIF1<0，且點(diǎn)SKIPIF1<0到SKIPIF1<0的漸近線的距離為SKIPIF1<0．(1)求雙曲線C的方程；(2)過點(diǎn)SKIPIF1<0作斜率不為SKIPIF1<0的直線SKIPIF1<0與雙曲線SKIPIF1<0交于M，N兩點(diǎn)，直線SKIPIF1<0分別交直線AM，AN于點(diǎn)E，F(xiàn)．試判斷以EF為直徑的圓是否經(jīng)過定點(diǎn)，若經(jīng)過定點(diǎn)，請(qǐng)求出定點(diǎn)坐標(biāo)；反之，請(qǐng)說明理由．考點(diǎn)三：拋物線【典例例題】例1．（2022·廣東惠州·一模）若拋物線SKIPIF1<0（SKIPIF1<0）上一點(diǎn)P（2，SKIPIF1<0）到其焦點(diǎn)的距離為4，則拋物線的標(biāo)準(zhǔn)方程為（

）A．y2=2x B．y2=4x C．y2=6x D．y2=8x例2．（2022·廣東韶關(guān)·一模）已知在平面直角坐標(biāo)系中，有兩定點(diǎn)SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0滿足SKIPIF1<0.(1)求動(dòng)點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)若拋物線SKIPIF1<0與軌跡SKIPIF1<0按順時(shí)針方向依次交于四點(diǎn)SKIPIF1<0（點(diǎn)SKIPIF1<0在第一象限）.①求證：直線SKIPIF1<0與直線SKIPIF1<0相交于SKIPIF1<0點(diǎn)；②設(shè)SKIPIF1<0的面積為S，求S取最大值時(shí)的拋物線方程.【方法技巧與總結(jié)】1.拋物線的定義：到準(zhǔn)線與到定點(diǎn)距離相等.2.拋物線的性質(zhì)：焦點(diǎn)弦長(zhǎng)【變式訓(xùn)練】1．（2022·廣東廣州·一模）設(shè)拋物線SKIPIF1<0的焦點(diǎn)為F，過點(diǎn)SKIPIF1<0的直線與E相交于A，B兩點(diǎn)，與E的準(zhǔn)線相交于點(diǎn)C，點(diǎn)B在線段AC上，SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0的面積之比SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·廣東廣東·一模）已知O為坐標(biāo)原點(diǎn)，F(xiàn)為拋物線SKIPIF1<0的焦點(diǎn)，P為C上一點(diǎn)，若SKIPIF1<0，則點(diǎn)F到直線PO的距離為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣東茂名·一模）（多選）已知拋物線C:SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，P是拋物線SKIPIF1<0上第一象限的點(diǎn)，SKIPIF1<0，直線PF與拋物線C的另一個(gè)交點(diǎn)為Q，則下列選項(xiàng)正確的是（

）A．點(diǎn)P的坐標(biāo)為（4，4）B．SKIPIF1<0C．SKIPIF1<0D．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)，則直線SKIPIF1<0的方程為：SKIPIF1<04．（2022·廣東·一模）（多選）已知拋物線SKIPIF1<0的焦點(diǎn)為F，拋物線C上存在n個(gè)點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）滿足SKIPIF1<0，則下列結(jié)論中正確的是（

）A．SKIPIF1<0時(shí)，SKIPIF1<0B．SKIPIF1<0時(shí)，SKIPIF1<0的最小值為9C．SKIPIF1<0時(shí)，SKIPIF1<0D．SKIPIF1<0時(shí)，SKIPIF1<0的最小值為85．（2022·廣東湛江·一模）（多選）已知F是拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)F作兩條互相垂直的直線SKIPIF1<0，SKIPIF1<0，SKIPIF1<0與C相交于A，B兩點(diǎn)，SKIPIF1<0與C相交于E，D兩點(diǎn)，M為A，B中點(diǎn)，N為E，D中點(diǎn)，直線l為拋物線C的準(zhǔn)線，則（

）A．點(diǎn)M到直線l的距離為定值 B．以SKIPIF1<0為直徑的圓與l相切C．SKIPIF1<0的最小值為32 D．當(dāng)SKIPIF1<0最小時(shí)，SKIPIF1<06．（2022·廣東深圳·一模）（多選）已知定圓A的半徑為1，圓心A到定直線l的距離為d，動(dòng)圓C與圓A和直線l都相切，圓心C的軌跡為如圖所示的兩條拋物線，記這兩拋物線的焦點(diǎn)到對(duì)應(yīng)準(zhǔn)線的距離分別為SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【鞏固練習(xí)】一、單選題1．橢圓SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，經(jīng)過點(diǎn)SKIPIF1<0的直線與橢圓SKIPIF1<0相交于A，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的周長(zhǎng)為16，則橢圓SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知橢圓SKIPIF1<0的左右焦點(diǎn)分別SKIPIF1<0，左頂點(diǎn)為A，上頂點(diǎn)為B，點(diǎn)P為橢圓上一點(diǎn)，且SKIPIF1<0，若SKIPIF1<0，則橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0分別為橢圓SKIPIF1<0的左右焦點(diǎn)，點(diǎn)P為橢圓上一點(diǎn)，以SKIPIF1<0為圓心的圓與直線SKIPIF1<0恰好相切于點(diǎn)P，則SKIPIF1<0是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．明朝的一個(gè)葡萄紋橢圓盤如圖（1）所示，清朝的一個(gè)青花山水樓閣紋飾橢圓盤如圖（2）所示，北宋的一個(gè)汝窯橢圓盤如圖（3）所示，這三個(gè)橢圓盤的外輪廊均為橢圓.已知圖（1）?（2）?（3）中橢圓的長(zhǎng)軸長(zhǎng)與短軸長(zhǎng)的比值分別SKIPIF1<0，設(shè)圖（1）?（2）?（3）中橢圓的離心率分別為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．設(shè)F為橢圓SKIPIF1<0的右焦點(diǎn)，點(diǎn)SKIPIF1<0，點(diǎn)B在C上，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．設(shè)橢圓SKIPIF1<0長(zhǎng)軸的兩個(gè)頂點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，點(diǎn)SKIPIF1<0為橢圓上不同于SKIPIF1<0、SKIPIF1<0的任一點(diǎn)，若將SKIPIF1<0的三個(gè)內(nèi)角記作SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，且滿足SKIPIF1<0，則橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知直線SKIPIF1<0過拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)，且與該拋物線交于SKIPIF1<0兩點(diǎn).若線段SKIPIF1<0的長(zhǎng)為16，SKIPIF1<0的中點(diǎn)到SKIPIF1<0軸距離為6，則SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）的面積是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08.過拋物線SKIPIF1<0的焦點(diǎn)F作直線l，交拋物線于A，B兩點(diǎn)，若SKIPIF1<0，則直線l的傾斜角等于（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．與p值有關(guān)二、多選題9．已知SKIPIF1<0為橢圓的焦點(diǎn)，SKIPIF1<0，SKIPIF1<0分別為橢圓的兩個(gè)頂點(diǎn)（且SKIPIF1<0不是離SKIPIF1<0最近的那個(gè)頂點(diǎn)），若SKIPIF1<0，SKIPIF1<0，則橢圓的離心率可以為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．設(shè)圓錐曲線C的兩個(gè)焦點(diǎn)分別為SKIPIF1<0，若曲線C上存在點(diǎn)P滿足SKIPIF1<0，則曲線C的離心率可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．23．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．24．已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，則（

）A．SKIPIF1<0的離心率為SKIPIF1<0 B．SKIPIF1<0的周長(zhǎng)為SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知拋物線C：SKIPIF1<0，過其準(zhǔn)線上的點(diǎn)T(1，-1)作C的兩條切線，切點(diǎn)分別為A、B，下列說法正確的是（

）A．p=1 B．拋物線的焦點(diǎn)為F(0，1)C．SKIPIF1<0 D．直線AB的斜率為SKIPIF1<0三、填空題1．與雙曲線SKIPIF1<0有相同的焦點(diǎn)，且短半軸長(zhǎng)為SKIPIF1<0的橢圓方程是________.2．已知橢圓SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0．過SKIPIF1<0且傾斜角為60°的直線交橢圓的上半部分于點(diǎn)SKIPIF1<0，以SKIPIF1<0，SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）為鄰邊作平行四邊形SKIPIF1<0