人教A版高二數(shù)學(xué)上學(xué)期重難點(diǎn)突破期末復(fù)習(xí)專題3.7直線與圓錐曲線的綜合問題（強(qiáng)化訓(xùn)練）（原卷版）

專題3.7直線與圓錐曲線的綜合問題題型一直線與圓錐曲線的位置關(guān)系題型二弦長問題題型三中點(diǎn)弦問題題型四定點(diǎn)問題題型五定值問題題型六定直線問題題型七三角形（四邊形）問題題型八求參數(shù)范圍問題題型九雙切線問題題型一 直線與圓錐曲線的位置關(guān)系1．直線l：SKIPIF1<0與橢圓C：SKIPIF1<0的位置關(guān)系是（

）A．相交 B．相切 C．相離 D．不能確定2．若直線SKIPIF1<0與橢圓SKIPIF1<0總有公共點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．直線SKIPIF1<0與雙曲線SKIPIF1<0的交點(diǎn)個數(shù)是（

）A．0 B．1 C．2 D．34．記雙曲線SKIPIF1<0的離心率為e，寫出滿足條件“直線SKIPIF1<0與C無公共點(diǎn)”的e的一個值為.5．直線SKIPIF1<0與雙曲線SKIPIF1<0有且只有一個公共點(diǎn)，則實(shí)數(shù)SKIPIF1<0．6．已知直線SKIPIF1<0與曲線SKIPIF1<0恰有一個公共點(diǎn)，則實(shí)數(shù)a的值為.7．如圖，已知直線SKIPIF1<0和橢圓SKIPIF1<0．m為何值時，直線l與橢圓C：

(1)有兩個公共點(diǎn)？(2)有且只有一個公共點(diǎn)？(3)沒有公共點(diǎn)？題型二 弦長問題8．已知橢圓的長軸長為SKIPIF1<0，焦點(diǎn)是SKIPIF1<0、SKIPIF1<0，點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0，過點(diǎn)SKIPIF1<0且傾斜角為SKIPIF1<0的直線SKIPIF1<0與橢圓交于SKIPIF1<0兩點(diǎn).(1)求橢圓的方程；(2)求線段SKIPIF1<0的長．9．直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，記SKIPIF1<0的面積為SKIPIF1<0.(1)當(dāng)SKIPIF1<0，SKIPIF1<0時，求SKIPIF1<0的取值范圍；(2)當(dāng)SKIPIF1<0，SKIPIF1<0時，求直線SKIPIF1<0的方程.10．已知雙曲線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，且其兩條漸近線相互垂直．(1)求雙曲線SKIPIF1<0的方程；(2)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與雙曲線SKIPIF1<0相交于不同的兩點(diǎn)SKIPIF1<0，若SKIPIF1<0的面積為SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），求直線SKIPIF1<0的方程．11．已知雙曲線SKIPIF1<0，焦點(diǎn)到漸近線的距離為SKIPIF1<0，且離心率為SKIPIF1<0．(1)求雙曲線SKIPIF1<0的方程；(2)直線SKIPIF1<0與雙曲線交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，求SKIPIF1<0的值．12．已知雙曲線SKIPIF1<0的焦距為6，且虛軸長是實(shí)軸長的SKIPIF1<0倍.(1)求雙曲線的方程；(2)過雙曲線的右焦點(diǎn)F且傾斜角為SKIPIF1<0的直線l與雙曲線交于A，B兩點(diǎn)，求SKIPIF1<0.13．已知拋物線SKIPIF1<0：SKIPIF1<0，坐標(biāo)原點(diǎn)為SKIPIF1<0，焦點(diǎn)為SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0.(1)若直線SKIPIF1<0與拋物線SKIPIF1<0只有一個公共點(diǎn)，求SKIPIF1<0的值；(2)過點(diǎn)SKIPIF1<0作斜率為SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0,SKIPIF1<0兩點(diǎn)，求SKIPIF1<0的面積．題型三 中點(diǎn)弦問題14．直線SKIPIF1<0過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，且與拋物線交于SKIPIF1<0兩點(diǎn)，線段SKIPIF1<0中點(diǎn)的縱坐標(biāo)為1，O為坐標(biāo)原點(diǎn)，則O到直線SKIPIF1<0的距離為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．設(shè)SKIPIF1<0，SKIPIF1<0為雙曲線SKIPIF1<0上兩點(diǎn)，下列四個點(diǎn)中，可為線段SKIPIF1<0中點(diǎn)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<016．（多選）已知橢圓SKIPIF1<0的焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，設(shè)直線l與橢圓C交于M，N兩點(diǎn)，且點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，則下列說法正確的是（

）A．SKIPIF1<0 B．橢圓C的離心率為SKIPIF1<0C．直線l的方程為SKIPIF1<0 D．SKIPIF1<0的周長為SKIPIF1<017．已知橢圓SKIPIF1<0的長軸長為SKIPIF1<0，SKIPIF1<0是SKIPIF1<0上一點(diǎn).(1)求E的方程；(2)若SKIPIF1<0是SKIPIF1<0上兩點(diǎn)，且線段SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，求SKIPIF1<0的值.18．在平面直角坐標(biāo)系SKIPIF1<0中，已知橢圓SKIPIF1<0：SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0為實(shí)數(shù)且SKIPIF1<0）與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).(1)若直線SKIPIF1<0過橢圓的右焦點(diǎn)，求SKIPIF1<0的面積；(2)線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，求直線SKIPIF1<0的斜率.19．已知拋物線SKIPIF1<0，過SKIPIF1<0的直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則直線SKIPIF1<0的方程為.20．已知雙曲線E：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，斜率為2的直線l與E的一條漸近線垂直，且交E于A，B兩點(diǎn)，SKIPIF1<0.(1)求E的方程；(2)設(shè)點(diǎn)P為線段AB的中點(diǎn)，求直線OP的方程.題型四 定點(diǎn)問題21．橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，左?右頂點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上.已知SKIPIF1<0面積的最大值為SKIPIF1<0，且SKIPIF1<0與SKIPIF1<0的面積之比為SKIPIF1<0.(1)求SKIPIF1<0的方程；(2)不垂直于坐標(biāo)軸的直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，SKIPIF1<0與SKIPIF1<0不重合，直線SKIPIF1<0與SKIPIF1<0的斜率之積為SKIPIF1<0.證明：SKIPIF1<0過定點(diǎn).22．已知SKIPIF1<0為橢圓SKIPIF1<0：SKIPIF1<0上一點(diǎn)，長軸長為SKIPIF1<0.(1)求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)不經(jīng)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若直線SKIPIF1<0與SKIPIF1<0的斜率之和為SKIPIF1<0，證明：直線SKIPIF1<0必過定點(diǎn)，并求出這個定點(diǎn)坐標(biāo).23．已知圓SKIPIF1<0，SKIPIF1<0為圓SKIPIF1<0內(nèi)一個定點(diǎn)，SKIPIF1<0是圓SKIPIF1<0上任意一點(diǎn)，線段SKIPIF1<0的垂直平分線SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，當(dāng)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動時.(1)求點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)已知圓SKIPIF1<0：SKIPIF1<0在SKIPIF1<0的內(nèi)部，SKIPIF1<0是SKIPIF1<0上不同的兩點(diǎn)，且直線SKIPIF1<0與圓SKIPIF1<0相切.求證：以SKIPIF1<0為直徑的圓過定點(diǎn).24．已知點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0上．(1)點(diǎn)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的左右頂點(diǎn)，SKIPIF1<0為雙曲線SKIPIF1<0上異于SKIPIF1<0，SKIPIF1<0的點(diǎn)，求SKIPIF1<0的值；(2)點(diǎn)SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上，且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為垂足，證明：存在定點(diǎn)SKIPIF1<0，使得SKIPIF1<0為定值．25．已知雙曲線SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0在雙曲線上，若SKIPIF1<0，且雙曲線焦距為4．(1)求雙曲線SKIPIF1<0的方程；(2)如果SKIPIF1<0為雙曲線SKIPIF1<0右支上的動點(diǎn)，在SKIPIF1<0軸負(fù)半軸上是否存在定點(diǎn)SKIPIF1<0使得SKIPIF1<0？若存在，求出點(diǎn)SKIPIF1<0的坐標(biāo)；若不存在，說明理由．26．在平面直角坐標(biāo)系SKIPIF1<0中，頂點(diǎn)在原點(diǎn)，以坐標(biāo)軸為對稱軸的拋物線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0.(1)求SKIPIF1<0的方程；(2)若SKIPIF1<0關(guān)于SKIPIF1<0軸對稱，焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0且與SKIPIF1<0軸不垂直的直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，求證：直線SKIPIF1<0過定點(diǎn).27．已知過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，過線段SKIPIF1<0的中點(diǎn)SKIPIF1<0作直線SKIPIF1<0軸，垂足為SKIPIF1<0，且SKIPIF1<0.(1)求拋物線SKIPIF1<0的方程；(2)若SKIPIF1<0為SKIPIF1<0上異于點(diǎn)SKIPIF1<0的任意一點(diǎn)，且直線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，證明：以SKIPIF1<0為直徑的圓過定點(diǎn).題型五 定值問題28．已知A，B為橢圓SKIPIF1<0的左、右頂點(diǎn)，過其焦點(diǎn)SKIPIF1<0的直線與橢圓SKIPIF1<0交于C，D兩點(diǎn)，并與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0(異于A，B)，直線SKIPIF1<0，SKIPIF1<0交于點(diǎn)SKIPIF1<0，求證：SKIPIF1<0為定值.29．已知橢圓SKIPIF1<0SKIPIF1<0離心率等于SKIPIF1<0且橢圓C經(jīng)過點(diǎn)SKIPIF1<0．(1)求橢圓的標(biāo)準(zhǔn)方程SKIPIF1<0；(2)若直線SKIPIF1<0與軌跡SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0的斜率之積等于SKIPIF1<0，試探求SKIPIF1<0的面積是否為定值，并說明理由．30．已知橢圓C：SKIPIF1<0過點(diǎn)SKIPIF1<0，且SKIPIF1<0．(1)求橢圓C的方程；(2)過點(diǎn)SKIPIF1<0的直線l交C于點(diǎn)M，N，直線SKIPIF1<0分別交直線SKIPIF1<0于點(diǎn)P，Q．求證：SKIPIF1<0為定值．31．已知F為拋物線C的焦點(diǎn)，過F的直線SKIPIF1<0交C于A，B兩點(diǎn)，點(diǎn)D在C上，使得SKIPIF1<0的重心G在x軸的正半軸上，直線SKIPIF1<0，SKIPIF1<0分別交SKIPIF1<0軸于Q，P兩點(diǎn).O為坐標(biāo)原點(diǎn)，當(dāng)SKIPIF1<0時，SKIPIF1<0.(1)求C的標(biāo)準(zhǔn)方程.(2)記P，G，Q的橫坐標(biāo)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，判斷SKIPIF1<0是否為定值.若是，求出該定值；若不是，請說明理由.32．在平面直角坐標(biāo)系SKIPIF1<0中，已知圓心為SKIPIF1<0的動圓過點(diǎn)SKIPIF1<0，且在SKIPIF1<0軸上截得的弦長為4，記SKIPIF1<0的軌跡為曲線SKIPIF1<0．(1)求曲線SKIPIF1<0的方程；(2)已知SKIPIF1<0及曲線SKIPIF1<0上的兩點(diǎn)SKIPIF1<0和SKIPIF1<0，直線SKIPIF1<0經(jīng)過定點(diǎn)SKIPIF1<0，直線SKIPIF1<0的斜率分別為SKIPIF1<0，求證：SKIPIF1<0為定值．33．已知雙曲線SKIPIF1<0：SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，離心率SKIPIF1<0.(1)求SKIPIF1<0的方程；(2)若直線SKIPIF1<0過點(diǎn)SKIPIF1<0且與SKIPIF1<0的右支交于M，N兩點(diǎn)，記SKIPIF1<0的左、右頂點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0為定值.34．已知雙曲線SKIPIF1<0過點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0．(1)求雙曲線的離心率；(2)過SKIPIF1<0的直線與雙曲線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，過雙曲線的右焦點(diǎn)SKIPIF1<0且與SKIPIF1<0平行的直線交雙曲線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，試問SKIPIF1<0是否為定值？若是定值，求該定值；若不是定值，請說明理由．題型六 定直線問題35．已知橢圓SKIPIF1<0：SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0的右焦點(diǎn)，三點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0中恰有兩點(diǎn)在橢圓SKIPIF1<0上.(1)求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)設(shè)點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0的左右端點(diǎn)，過點(diǎn)SKIPIF1<0作直線交橢圓SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)（不同于SKIPIF1<0），求證：直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)SKIPIF1<0在定直線上運(yùn)動，并求出該直線的方程.36．已知橢圓SKIPIF1<0：SKIPIF1<0的短軸長為SKIPIF1<0，離心率為SKIPIF1<0．(1)求橢圓SKIPIF1<0的方程；(2)過點(diǎn)SKIPIF1<0的動直線SKIPIF1<0與橢圓SKIPIF1<0相交于不同的SKIPIF1<0兩點(diǎn)，在線段SKIPIF1<0上取點(diǎn)SKIPIF1<0，滿足SKIPIF1<0，證明：點(diǎn)SKIPIF1<0總在某定直線上．37．已知點(diǎn)A為圓SKIPIF1<0上任意一點(diǎn)，點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，線段SKIPIF1<0的垂直平分線與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0．(1)求點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)設(shè)軌跡E與SKIPIF1<0軸分別交于SKIPIF1<0兩點(diǎn)（SKIPIF1<0在SKIPIF1<0的左側(cè)），過SKIPIF1<0的直線SKIPIF1<0與軌跡SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0與直線SKIPIF1<0的交于SKIPIF1<0，證明：SKIPIF1<0在定直線上．38．已知點(diǎn)SKIPIF1<0，SKIPIF1<0，動點(diǎn)SKIPIF1<0滿足直線SKIPIF1<0與SKIPIF1<0的斜率之積為SKIPIF1<0，記動點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0．(1)求曲線SKIPIF1<0的方程；(2)過點(diǎn)SKIPIF1<0的直線與曲線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0與SKIPIF1<0相交于SKIPIF1<0．求證：點(diǎn)SKIPIF1<0在定直線上．39．在平面直角坐標(biāo)系SKIPIF1<0中，已知雙曲線Ｃ的中心為坐標(biāo)原點(diǎn)，對稱軸是坐標(biāo)軸，右支與x軸的交點(diǎn)為SKIPIF1<0，其中一條漸近線的傾斜角為SKIPIF1<0.(1)求C的標(biāo)準(zhǔn)方程；(2)過點(diǎn)SKIPIF1<0作直線l與雙曲線C的左右兩支分別交于A，B兩點(diǎn)，在線段SKIPIF1<0上取一點(diǎn)E滿足SKIPIF1<0，證明：點(diǎn)E在一條定直線上.40．如圖，正六邊形ABCDEF的邊長為4．已知雙曲線SKIPIF1<0的焦點(diǎn)分別為A，D，兩條漸近線分別為直線BE，CF．

(1)建立適當(dāng)?shù)钠矫嬷苯亲鴺?biāo)系，求SKIPIF1<0的方程；(2)過點(diǎn)A的直線l與SKIPIF1<0交于P，Q兩點(diǎn)，SKIPIF1<0，若點(diǎn)M滿足SKIPIF1<0，證明：點(diǎn)M在一條定直線上．41．已知拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0的兩條直線SKIPIF1<0、SKIPIF1<0分別交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)和SKIPIF1<0、SKIPIF1<0兩點(diǎn)．當(dāng)SKIPIF1<0的斜率為SKIPIF1<0時，SKIPIF1<0．(1)求SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)設(shè)SKIPIF1<0為直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)，證明：點(diǎn)SKIPIF1<0在定直線上．題型七 三角形（四邊形）問題42．已知SKIPIF1<0分別為雙曲線SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0是雙曲線SKIPIF1<0右支上(頂點(diǎn)除外)任意一點(diǎn)，若SKIPIF1<0的角平分線與以SKIPIF1<0為直徑的圓交于點(diǎn)SKIPIF1<0，則SKIPIF1<0的面積的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<043．已知SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，點(diǎn)SKIPIF1<0在該拋物線上且位于SKIPIF1<0軸的兩側(cè)，SKIPIF1<0（其中SKIPIF1<0為坐標(biāo)原點(diǎn)），則SKIPIF1<0與SKIPIF1<0面積之和的最小值是．44．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，點(diǎn)SKIPIF1<0在C上，O為坐標(biāo)原點(diǎn).(1)求C的方程;(2)已知直線SKIPIF1<0，l與C有兩個交點(diǎn)A，B，線段AB的中點(diǎn)為M.①證明：直線OM的斜率與直線l的斜率的乘積為定值.②若SKIPIF1<0，求△OAB面積的最大值，并求此時直線l的方程.45．設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0上點(diǎn)SKIPIF1<0滿足SKIPIF1<0.(1)求拋物線SKIPIF1<0的方程；(2)已知正方形SKIPIF1<0有三個頂點(diǎn)在拋物線SKIPIF1<0上，求該正方形面積的最小值.46．已知橢圓C：SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，左頂點(diǎn)為D，離心率為SKIPIF1<0，經(jīng)過SKIPIF1<0的直線交橢圓于A，B兩點(diǎn)，SKIPIF1<0的周長為8.(1)求橢圓C的方程；(2)過直線SKIPIF1<0上一點(diǎn)P作橢圓C的兩條切線，切點(diǎn)分別為M，N，①證明：直線MN過定點(diǎn)；②求SKIPIF1<0的最大值.47．在平面直角坐標(biāo)系SKIPIF1<0中，已知點(diǎn)SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0.記SKIPIF1<0的軌跡為SKIPIF1<0.(1)求SKIPIF1<0的方程；(2)直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上的兩點(diǎn)，若四邊形SKIPIF1<0的對角線SKIPIF1<0，求四邊形SKIPIF1<0面積的最大值.48．已知雙曲線SKIPIF1<0：SKIPIF1<0，雙曲線SKIPIF1<0與SKIPIF1<0共漸近線且經(jīng)過點(diǎn)SKIPIF1<0

(1)求雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程．(2)如圖所示，點(diǎn)SKIPIF1<0是曲線SKIPIF1<0上任意一動點(diǎn)（第一象限），直線SKIPIF1<0軸于點(diǎn)SKIPIF1<0，SKIPIF1<0軸于點(diǎn)SKIPIF1<0，直線SKIPIF1<0交曲線SKIPIF1<0于點(diǎn)SKIPIF1<0（第一象限），過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線交SKIPIF1<0于點(diǎn)SKIPIF1<0，交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，求SKIPIF1<0的最小值．題型八 求參數(shù)范圍問題49．已知SKIPIF1<0是拋物線SKIPIF1<0上三個動點(diǎn)，且SKIPIF1<0的重心為拋物線的焦點(diǎn)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0兩點(diǎn)均在SKIPIF1<0軸上方，若SKIPIF1<0的斜率SKIPIF1<0恒成立，則m的最大值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<050．已知橢圓C：SKIPIF1<0的上、下頂點(diǎn)分別為A，B，左頂點(diǎn)為D，SKIPIF1<0是面積為SKIPIF1<0的正三角形．(1)求橢圓C的方程；(2)過橢圓外一點(diǎn)SKIPIF1<0的直線交橢圓于P，Q兩點(diǎn)，已知點(diǎn)P與點(diǎn)SKIPIF1<0關(guān)于x軸對稱，直線SKIPIF1<0與x軸交于點(diǎn)K；若SKIPIF1<0是鈍角，求m的取值范圍．51．已知橢圓C：SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，若點(diǎn)SKIPIF1<0在橢圓上，且SKIPIF1<0為等邊三角形．(1)求橢圓C的標(biāo)準(zhǔn)方程？(2)過點(diǎn)SKIPIF1<0且斜率為k的直線l與橢圓C交于A、B兩點(diǎn)，若SKIPIF1<0為鈍角，求k的取值范圍．52．已知動點(diǎn)SKIPIF1<0到定點(diǎn)SKIPIF1<0的距離與動點(diǎn)SKIPIF1<0到定直線SKIPIF1<0的距離之比為SKIPIF1<0．(1)求點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)對SKIPIF1<0，曲線SKIPIF1<0上是否始終存在兩點(diǎn)SKIPIF1<0，SKIPIF1<0關(guān)于直線SKIPIF1<0對稱？若存在，求實(shí)數(shù)SKIPIF1<0的取值范圍；若不存在，請說明理由．53．已知雙曲線SKIPIF1<0與直線SKIPIF1<0有唯一的公共點(diǎn)．(1)點(diǎn)SKIPIF1<0在直線l上，求直線l的方程；(2)設(shè)點(diǎn)SKIPIF1<0分別為雙曲線C的左右焦點(diǎn)，E為右頂點(diǎn)，過點(diǎn)SKIPIF1<0的直線與雙曲線C的右支交于A，B兩點(diǎn)（其中點(diǎn)A在第一象限），設(shè)M，N分別為SKIPIF1<0的內(nèi)心．①點(diǎn)M的橫坐標(biāo)是否為定值？若是，求出橫坐標(biāo)的值；若不是，請說明理由．②求SKIPIF1<0的取值范圍．54．已知雙曲線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）上一點(diǎn)SKIPIF1<0到SKIPIF1<0的兩條漸近線的距離之積為SKIPIF1<0．(1)求SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)若直線SKIPIF1<0與SKIPIF1<0有兩個不同的交點(diǎn)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0的內(nèi)心恒在直線SKIPIF1<0上，求SKIPIF1<0在SKIPIF1<0軸上的截距的取值范圍．55．曲線SKIPIF1<0，第一象限內(nèi)點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0的縱坐標(biāo)是SKIPIF1<0．(1)若SKIPIF1<0到準(zhǔn)線距離為3，求SKIPIF1<0；(2)若SKIPIF1<0在SKIPIF1<0軸上，SKIPIF1<0中點(diǎn)在SKIPIF1<0上，求點(diǎn)SKIPIF1<0坐標(biāo)和坐標(biāo)原點(diǎn)SKIPIF1<0到SKIPIF1<0距離；(3)直線SKIPIF1<0，令SKIPIF1<0是第一象限SKIPIF1<0上異于SKIPIF1<0的一點(diǎn)，直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0是SKIPIF1<0在SKIPIF1<0上的投影，若點(diǎn)SKIPIF1<0滿足“對于任意SKIPIF1<0都有SKIPIF1<0”求SKIPIF1<0的取值范圍．題型九 雙切線問題56．已知點(diǎn)SKIPIF1<0到直線SKIPIF1<0：SKIPIF1<0的距離和它到定點(diǎn)SKIPIF1<0的距離之比為常數(shù)SKIPIF1<0．(1)求點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)若點(diǎn)SKIPIF1<0是直線SKIPIF1<0上一點(diǎn)，過SKIPIF1<0作曲線SKIPIF1<0的兩條切線分別切于點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0，試求三角形SKIPIF1<0面積的最小值．（二次曲線SKIPIF1<0在其上一點(diǎn)SKIPIF1<0處的切線為SKIPIF1<0）57．在橢圓SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）中，其所有外切矩形的頂點(diǎn)在一個定圓SKIPIF1<0：SKIPIF1<0上，稱此圓為橢圓的蒙日圓.橢圓SKIPIF1<0過SKIPIF1<0，SKIPIF1<0.(1)求橢圓SKIPIF1<0的方程；(2)過橢圓SKIPIF1<0的蒙日圓上一點(diǎn)SKIPIF1<0，作橢圓的一條切線，與蒙日圓交于另一點(diǎn)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0存在，證明：SKIPIF1<0為定值.58．已知橢圓SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，左右頂點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0上異于SKIPIF1<0、SKIPIF1<0的任意一點(diǎn)，SKIPIF1<0、SKIPIF1<0斜率之積為SKIPIF1<0，且SKIPIF1<0的面積最大值為SKIPIF1<0.

(1)求橢圓SKIPIF1<0的方程；(2)直線SKIPIF1<0交橢圓SKIPIF1<0于另一點(diǎn)SKIPIF1<0，分別過SKIPIF1<0、SKIPIF1<0