新高考數(shù)學(xué)二輪復(fù)習(xí)核心考點(diǎn)講與練重難點(diǎn)13六種雙曲線解題方法原卷版

重難點(diǎn)13六種雙曲線解題方法（核心考點(diǎn)講與練）題型一：待定系數(shù)法求雙曲線方程一、單選題1．（2022·河南·模擬預(yù)測（文））已知雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，一條漸近線方程為SKIPIF1<0，過雙曲線C的右焦點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線SKIPIF1<0交雙曲線的右支于A，B兩點(diǎn)，若SKIPIF1<0的周長為36，則雙曲線C的標(biāo)準(zhǔn)方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川·宜賓市教科所三模（理））若等軸雙曲線的焦距為4，則它的一個(gè)頂點(diǎn)到一條漸近線的距離為（

）A．1 B．SKIPIF1<0 C．2 D．33．（2022·寧夏·石嘴山市第一中學(xué)三模（理））雙曲線E與橢圓SKIPIF1<0焦點(diǎn)相同且離心率是橢圓C離心率的SKIPIF1<0倍，則雙曲線E的標(biāo)準(zhǔn)方程為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·內(nèi)蒙古包頭·二模（理））已知SKIPIF1<0，SKIPIF1<0是雙曲線SKIPIF1<0的兩個(gè)焦點(diǎn)，R是C上的一點(diǎn)，且SKIPIF1<0，SKIPIF1<0，C經(jīng)過點(diǎn)SKIPIF1<0，則C的實(shí)軸長為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．6 D．3二、多選題5．（2022·江蘇·揚(yáng)州中學(xué)高三階段練習(xí)）已知雙曲線SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，兩條漸近線的夾角正切值為SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0與雙曲線SKIPIF1<0的右支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，設(shè)SKIPIF1<0的內(nèi)心為SKIPIF1<0，則（

）A．雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程為SKIPIF1<0 B．滿足SKIPIF1<0的直線SKIPIF1<0有2條C．SKIPIF1<0 D．SKIPIF1<0與SKIPIF1<0的面積的比值的取值范圍是SKIPIF1<06．（2022·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0，其焦點(diǎn)SKIPIF1<0到漸近線的距離為SKIPIF1<0，則下列說法正確的是（

）A．雙曲線SKIPIF1<0的方程為SKIPIF1<0 B．雙曲線SKIPIF1<0的漸近線方程為SKIPIF1<0C．雙曲線SKIPIF1<0的離心率為SKIPIF1<0 D．雙曲線SKIPIF1<0上的點(diǎn)到焦點(diǎn)距離的最小值為SKIPIF1<07．（2022·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的一條漸近線的方程為SKIPIF1<0，且過點(diǎn)SKIPIF1<0，橢圓SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）的焦距與雙曲線SKIPIF1<0的焦距相同，且橢圓SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，過SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0（SKIPIF1<0），SKIPIF1<0兩點(diǎn)，則下列敘述正確的是（

）A．雙曲線的離心率為2B．雙曲線的實(shí)軸長為SKIPIF1<0C．點(diǎn)SKIPIF1<0的橫坐標(biāo)的取值范圍為SKIPIF1<0D．點(diǎn)SKIPIF1<0的橫坐標(biāo)的取值范圍為SKIPIF1<0三、填空題8．（2022·福建寧德·模擬預(yù)測）若過點(diǎn)SKIPIF1<0的雙曲線的漸近線為SKIPIF1<0，則該雙曲線的標(biāo)準(zhǔn)方程是___________.四、解答題9．（2022·全國·模擬預(yù)測）已知雙曲線SKIPIF1<0的一條漸近線的傾斜角為SKIPIF1<0，點(diǎn)SKIPIF1<0在雙曲線E上.(1)求雙曲線E的標(biāo)準(zhǔn)方程；(2)若動(dòng)直線l與雙曲線E相切，過點(diǎn)SKIPIF1<0作直線l的垂線，垂足為H，試判斷SKIPIF1<0是否為定值？如果是，請求出該值；如果不是，請說明理由.10．（2022·上海市七寶中學(xué)高三期中）雙曲線SKIPIF1<0：SKIPIF1<0（a＞0，b＞0）經(jīng)過點(diǎn)SKIPIF1<0，且漸近線方程為SKIPIF1<0．(1)求SKIPIF1<0，SKIPIF1<0的值；(2)點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是雙曲線SKIPIF1<0上不同的三點(diǎn)，且SKIPIF1<0，SKIPIF1<0兩點(diǎn)關(guān)于SKIPIF1<0軸對稱，SKIPIF1<0的外接圓經(jīng)過原點(diǎn)SKIPIF1<0．求證：點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0的縱坐標(biāo)互為倒數(shù)；(3)在（2）的條件下，試問是否存在一個(gè)定圓與直線SKIPIF1<0相切，若有，求出定圓方程，沒有說明理由．11．（2022·全國·高三專題練習(xí)）如圖，已知雙曲線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）的右焦點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0分別在SKIPIF1<0的兩條漸近線上，SKIPIF1<0軸，SKIPIF1<0∥SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）.(1)求雙曲線SKIPIF1<0的方程；(2)過SKIPIF1<0上一點(diǎn)SKIPIF1<0的直線SKIPIF1<0與直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0，與直線SKIPIF1<0相交于點(diǎn)SKIPIF1<0，證明：當(dāng)點(diǎn)SKIPIF1<0在SKIPIF1<0上移動(dòng)時(shí)，SKIPIF1<0恒為定值，并求此定值.12．（2022·河北衡水中學(xué)一模）在平面直角坐標(biāo)系SKIPIF1<0中，雙曲線SKIPIF1<0的離心率為SKIPIF1<0，實(shí)軸長為4.(1)求C的方程；(2)如圖，點(diǎn)A為雙曲線的下頂點(diǎn)，直線l過點(diǎn)SKIPIF1<0且垂直于y軸（P位于原點(diǎn)與上頂點(diǎn)之間），過P的直線交C于G，H兩點(diǎn)，直線AG，AH分別與l交于M，N兩點(diǎn)，若O，A，N，M四點(diǎn)共圓，求點(diǎn)P的坐標(biāo).13．（2022·河南·三模（理））已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等差數(shù)列，過SKIPIF1<0的直線交雙曲線SKIPIF1<0于SKIPIF1<0?SKIPIF1<0兩點(diǎn)，若雙曲線SKIPIF1<0過點(diǎn)SKIPIF1<0.(1)求雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)過雙曲線SKIPIF1<0的左頂點(diǎn)SKIPIF1<0作直線SKIPIF1<0?SKIPIF1<0，分別與直線SKIPIF1<0交于SKIPIF1<0?SKIPIF1<0兩點(diǎn)，是否存在實(shí)數(shù)SKIPIF1<0，使得以SKIPIF1<0為直徑的圓恒過SKIPIF1<0，若存在，求出SKIPIF1<0的值；若不存在，請說明理由.題型二：相同漸近線雙曲線方程求法一、單選題1．（2022·浙江嘉興·模擬預(yù)測）已知雙曲線C的漸近線方程為SKIPIF1<0，且焦距為10，則雙曲線C的標(biāo)準(zhǔn)方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2020·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0與雙曲線SKIPIF1<0有公共的漸近線，且經(jīng)過點(diǎn)SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．23．（2020·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0的一個(gè)焦點(diǎn)為SKIPIF1<0，且與雙曲線SKIPIF1<0的漸近線相同，則雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2020·全國·高三階段練習(xí)）已知雙曲線SKIPIF1<0過點(diǎn)SKIPIF1<0且漸近線為SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0的方程為SKIPIF1<0 B．SKIPIF1<0的離心率為2C．曲線SKIPIF1<0經(jīng)過SKIPIF1<0的一個(gè)焦點(diǎn) D．直線SKIPIF1<0與SKIPIF1<0有兩個(gè)公共點(diǎn)5．（2021·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，一條漸近線過點(diǎn)SKIPIF1<0，則下列結(jié)論正確的是（

）A．雙曲線SKIPIF1<0的離心率為SKIPIF1<0B．雙曲線SKIPIF1<0與雙曲線SKIPIF1<0有相同的漸近線C．若SKIPIF1<0到漸近線的距離為2，則雙曲線SKIPIF1<0的方程為SKIPIF1<0D．若直線SKIPIF1<0與漸近線圍成的三角形面積為SKIPIF1<0則焦距為SKIPIF1<0三、填空題6．（2022·遼寧·模擬預(yù)測）焦點(diǎn)在SKIPIF1<0軸上的雙曲線SKIPIF1<0與雙曲線SKIPIF1<0有共同的漸近線，且SKIPIF1<0的焦點(diǎn)到一條漸近線的距離為SKIPIF1<0，則雙曲線SKIPIF1<0的方程為______．7．（2022·全國·高三專題練習(xí)）若雙曲線SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）與雙曲線SKIPIF1<0有相同的漸近線，且SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，則SKIPIF1<0的實(shí)軸長為_________四、解答題8．（2022·全國·高三專題練習(xí)）已知雙曲線SKIPIF1<0與SKIPIF1<0有相同的漸近線，點(diǎn)SKIPIF1<0為SKIPIF1<0的右焦點(diǎn)，SKIPIF1<0為SKIPIF1<0的左，右頂點(diǎn).（1）求雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）若直線SKIPIF1<0過點(diǎn)SKIPIF1<0交雙曲線SKIPIF1<0的右支于SKIPIF1<0兩點(diǎn)，設(shè)直線SKIPIF1<0斜率分別為SKIPIF1<0，是否存在實(shí)數(shù)入使得SKIPIF1<0?若存在，求出SKIPIF1<0的值；若不存在，請說明理由.題型三：直接法解決離心率問題一、單選題1．（2022·廣東·佛山市南海區(qū)藝術(shù)高級中學(xué)模擬預(yù)測）已知雙曲線的方程SKIPIF1<0，則該雙曲線的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江·哈九中模擬預(yù)測（理））如圖1所示，雙曲線具有光學(xué)性質(zhì)：從雙曲線右焦點(diǎn)發(fā)出的光線經(jīng)過雙曲線鏡面反射，其反射光線的反向延長線經(jīng)過雙曲線的左焦點(diǎn)．若雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，從SKIPIF1<0發(fā)出的光線經(jīng)過圖2中的A，B兩點(diǎn)反射后，分別經(jīng)過點(diǎn)SKIPIF1<0和SKIPIF1<0．且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江金華·三模）已知雙曲線C：SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0為雙曲線SKIPIF1<0的左焦點(diǎn)，若SKIPIF1<0的右支上存在一點(diǎn)SKIPIF1<0，使得SKIPIF1<0外接圓SKIPIF1<0的半徑為SKIPIF1<0，且四邊形SKIPIF1<0為菱形，則雙曲線SKIPIF1<0的離心率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·重慶八中高三階段練習(xí)）如圖，已知SKIPIF1<0，SKIPIF1<0為雙曲線SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)，過點(diǎn)SKIPIF1<0，SKIPIF1<0分別作直線SKIPIF1<0，SKIPIF1<0交雙曲線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0四點(diǎn)，使得四邊形SKIPIF1<0為平行四邊形，且以SKIPIF1<0為直徑的圓過SKIPIF1<0，SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·貴州黔東南·一模（理））已知雙曲線SKIPIF1<0，直線SKIPIF1<0與C交于A、B兩點(diǎn)（A在B的上方），SKIPIF1<0，點(diǎn)E在y軸上，且SKIPIF1<0軸．若SKIPIF1<0的內(nèi)心到y(tǒng)軸的距離為SKIPIF1<0，則C的離心率為（

）.A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題6．（2022·山東煙臺(tái)·一模）已知雙曲線C：SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為C的左、右焦點(diǎn)，則（

）A．雙曲線SKIPIF1<0和C的離心率相等B．若P為C上一點(diǎn)，且SKIPIF1<0，則SKIPIF1<0的周長為SKIPIF1<0C．若直線SKIPIF1<0與C沒有公共點(diǎn)，則SKIPIF1<0或SKIPIF1<0D．在C的左、右兩支上分別存在點(diǎn)M，N使得SKIPIF1<0三、填空題7．（2022·安徽·合肥一中模擬預(yù)測（理））已知雙曲線C：SKIPIF1<0（SKIPIF1<0），以C的焦點(diǎn)為圓心，3為半徑的圓與C的漸近線相交，則雙曲線C的離心率的取值范圍是________________．8．（2022·山東日照·二模）如圖1所示，雙曲線具有光學(xué)性質(zhì)：從雙曲線右焦點(diǎn)發(fā)出的光線經(jīng)過雙曲線鏡面反射，其反射光線的反向延長線經(jīng)過雙曲線的左焦點(diǎn).若雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，從SKIPIF1<0發(fā)出的光線經(jīng)過圖2中的A，B兩點(diǎn)反射后，分別經(jīng)過點(diǎn)C和D，且SKIPIF1<0，SKIPIF1<0，則E的離心率為___________.9．（2022·浙江·三模）已知雙曲線SKIPIF1<0的兩個(gè)焦點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0是雙曲線第一象限上一點(diǎn)，在點(diǎn)P處作雙曲線C的切線l，若點(diǎn)SKIPIF1<0到切線l的距離之積為3，則雙曲線C的離心率為_______．四、解答題10．（2022·河北張家口·三模）已知SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)P滿足SKIPIF1<0，點(diǎn)P的軌跡為曲線C.(1)求曲線C的方程；(2)直線SKIPIF1<0與曲線C相切，與曲線SKIPIF1<0交于M?N兩點(diǎn)，且SKIPIF1<0（O為坐標(biāo)原點(diǎn)），求曲線E的離心率.題型四：構(gòu)造齊次方程法求離心率的值或范圍一、單選題1．（2022·湖北省天門中學(xué)模擬預(yù)測）已知共焦點(diǎn)的橢圓和雙曲線，焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，記它們其中的一個(gè)交點(diǎn)為P，且SKIPIF1<0，則該橢圓離心率SKIPIF1<0與雙曲線離心率SKIPIF1<0必定滿足的關(guān)系式為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·浙江·赫威斯育才高中模擬預(yù)測）已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，過SKIPIF1<0的直線SKIPIF1<0與雙曲線SKIPIF1<0左、右支分別交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，SKIPIF1<0的面積為SKIPIF1<0，雙曲線SKIPIF1<0的離心率為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．2C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江·模擬預(yù)測）已知雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，M為右支上一點(diǎn)，SKIPIF1<0的內(nèi)切圓圓心為Q，直線SKIPIF1<0交x軸于點(diǎn)N，SKIPIF1<0，則雙曲線的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2022·全國·模擬預(yù)測）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的一條漸近線，以SKIPIF1<0為圓心，SKIPIF1<0為半徑的圓與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則（

）A．過點(diǎn)SKIPIF1<0且與圓SKIPIF1<0相切的直線與雙曲線SKIPIF1<0沒有公共點(diǎn)B．SKIPIF1<0的離心率的最大值是SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0的離心率的取值范圍是SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0的離心率為SKIPIF1<0三、雙空題5．（2022·湖北武漢·模擬預(yù)測）已知SKIPIF1<0，SKIPIF1<0，是雙曲線C：SKIPIF1<0的左右焦點(diǎn)，過SKIPIF1<0的直線與雙曲線左支交于點(diǎn)A，與右支交于點(diǎn)B，SKIPIF1<0與SKIPIF1<0內(nèi)切圓的圓心分別為SKIPIF1<0，SKIPIF1<0，半徑分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的橫坐標(biāo)為__________；若SKIPIF1<0，則雙曲線離心率為__________.四、填空題6．（2022·河北·模擬預(yù)測）已知SKIPIF1<0分別為雙曲線SKIPIF1<0的左?右焦點(diǎn)，過點(diǎn)SKIPIF1<0的直線與雙曲線SKIPIF1<0的左?右兩支分別交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則雙曲線SKIPIF1<0的離心率是__________．7．（2022·福建三明·模擬預(yù)測）已知雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0?SKIPIF1<0，雙曲線上一點(diǎn)A關(guān)于原點(diǎn)O對稱的點(diǎn)為B，且滿足SKIPIF1<0，SKIPIF1<0，則該雙曲線的離心率為___________.8．（2022·安徽馬鞍山·三模（文））已知雙曲線E的焦點(diǎn)在x軸上，中心為坐標(biāo)原點(diǎn)，F(xiàn)為E的右焦點(diǎn)，過點(diǎn)F作直線SKIPIF1<0與E的左右兩支分別交于A，B兩點(diǎn)，過點(diǎn)F作直線SKIPIF1<0與E的右支交于C，D兩點(diǎn)，若點(diǎn)B恰為SKIPIF1<0的重心，且SKIPIF1<0為等腰直角三角形，則雙曲線E的離心率為___________.五、解答題9．（2022·全國·高三專題練習(xí)）設(shè)SKIPIF1<0，SKIPIF1<0為雙曲線SKIPIF1<0SKIPIF1<0的左、右頂點(diǎn)，直線SKIPIF1<0過右焦點(diǎn)SKIPIF1<0且與雙曲線SKIPIF1<0的右支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，當(dāng)直線SKIPIF1<0垂直于SKIPIF1<0軸時(shí)，SKIPIF1<0為等腰直角三角形.（1）求雙曲線SKIPIF1<0的離心率；（2）已知直線SKIPIF1<0，SKIPIF1<0分別交直線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，當(dāng)直線SKIPIF1<0的傾斜角變化時(shí)，以SKIPIF1<0為直徑的圓是否過定點(diǎn)，若過定點(diǎn)，求出定點(diǎn)的坐標(biāo)；若不過定點(diǎn)，請說明理由.10．（2021·全國·高三專題練習(xí)）設(shè)雙曲線SKIPIF1<0的方程為SKIPIF1<0，SKIPIF1<0、SKIPIF1<0為其左?右兩個(gè)頂點(diǎn)，SKIPIF1<0是雙曲線SKIPIF1<0上的任意一點(diǎn)，引SKIPIF1<0，SKIPIF1<0，SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0.（1）求SKIPIF1<0點(diǎn)的軌跡方程；（2）設(shè)（1）中所求軌跡為SKIPIF1<0，SKIPIF1<0、SKIPIF1<0的離心率分別為SKIPIF1<0、SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的取值范圍.題型五：漸近線綜合問題一、單選題1．（2022·安徽·安慶一中高三階段練習(xí)（文））已知SKIPIF1<0為坐標(biāo)原點(diǎn)，雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，離心率SKIPIF1<0，過SKIPIF1<0的直線與SKIPIF1<0的兩條漸近線的交點(diǎn)分別為SKIPIF1<0為直角三角形，SKIPIF1<0，則SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·山西呂梁·三模（文））已知雙曲線SKIPIF1<0的離心率SKIPIF1<0是它的一條漸近線斜率的2倍，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．23．（2022·江西宜春·模擬預(yù)測（文））若雙曲線SKIPIF1<0的一個(gè)頂點(diǎn)為A，過點(diǎn)A的直線SKIPIF1<0與雙曲線只有一個(gè)公共點(diǎn)，則該雙曲線的焦距為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川遂寧·模擬預(yù)測（文））設(shè)雙曲線C：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的左、右焦點(diǎn)是SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為原點(diǎn)，若以SKIPIF1<0為直徑的圓與C的漸近線的一個(gè)交點(diǎn)為P，且SKIPIF1<0，則C的漸近線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·海南·模擬預(yù)測）已知雙曲線SKIPIF1<0的一條漸近線與直線SKIPIF1<0垂直，則SKIPIF1<0的焦點(diǎn)坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題6．（2022·福建南平·三模）已知雙曲線SKIPIF1<0的方程為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0分別為雙曲線SKIPIF1<0的左?右焦點(diǎn)，過SKIPIF1<0且與x軸垂直的直線交雙曲線SKIPIF1<0于M，N兩點(diǎn)，又SKIPIF1<0，則（

）A．雙曲線SKIPIF1<0的漸近線方程為SKIPIF1<0B．雙曲線SKIPIF1<0的頂點(diǎn)到兩漸近線距離的積的5倍等于焦點(diǎn)到漸近線距離的平方C．雙曲線SKIPIF1<0的實(shí)軸長?虛軸長?焦距成等比數(shù)列D．雙曲線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，滿足SKIPIF1<07．（2022·湖南·一模）已知雙曲線SKIPIF1<0的左焦點(diǎn)為F，過點(diǎn)F作C的一條漸近線的平行線交C于點(diǎn)A，交另一條漸近線于點(diǎn)B．若SKIPIF1<0，則下列說法正確的是（

）A．雙曲線C的漸近線方程為SKIPIF1<0 B．雙曲線C的離心率為SKIPIF1<0C．點(diǎn)A到兩漸近線的距離的乘積為SKIPIF1<0 D．O為坐標(biāo)原點(diǎn)，則SKIPIF1<08．（2022·全國·高三專題練習(xí)）下列雙曲線的漸近線方程為SKIPIF1<0的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題9．（2022·全國·模擬預(yù)測）已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左?右焦點(diǎn)，則下列說法正確的序號(hào)是___________.①SKIPIF1<0；②若SKIPIF1<0，則雙曲線C的離心率為SKIPIF1<0；③若點(diǎn)P在雙曲線C的右支上，SKIPIF1<0與y軸交于M，SKIPIF1<0，則SKIPIF1<0；④若雙曲線C的離心率為SKIPIF1<0，則兩條漸近線夾角余弦值為SKIPIF1<0.四、解答題10．（2022·全國·模擬預(yù)測）已知雙曲線SKIPIF1<0的一條漸近線SKIPIF1<0的方程為SKIPIF1<0，且右焦點(diǎn)SKIPIF1<0到SKIPIF1<0的距離為1．(1)求雙曲線SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)若點(diǎn)SKIPIF1<0為直線SKIPIF1<0上一點(diǎn)，傾斜角為SKIPIF1<0的直線SKIPIF1<0與雙曲線SKIPIF1<0的右支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0為等邊三角形，求直線SKIPIF1<0在SKIPIF1<0軸上的截距．題型六：利用自變量范圍求離心率范圍一、單選題1．（2022·山西太原·二模（理））已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，點(diǎn)Q為雙曲線左支上一動(dòng)點(diǎn)，圓SKIPIF1<0與y軸的一個(gè)交點(diǎn)為P，若SKIPIF1<0，則雙曲線離心率的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）已知雙曲線C：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的右焦點(diǎn)F（SKIPIF1<0，0），點(diǎn)Q是雙曲線C的左支上一動(dòng)點(diǎn)，圓E：SKIPIF1<0與y軸的一個(gè)交點(diǎn)為P