第第頁(yè)第14講雙曲線(xiàn)【題型歸納目錄】題型一：雙曲線(xiàn)的定義、條件題型二：求雙曲線(xiàn)的標(biāo)準(zhǔn)方程題型三：雙曲線(xiàn)的綜合問(wèn)題題型四：軌跡方程題型五：雙曲線(xiàn)的簡(jiǎn)單幾何性質(zhì)題型六：求雙曲線(xiàn)的離心率題型七：求雙曲線(xiàn)離心率的取值范圍題型八：由雙曲線(xiàn)離心率求參數(shù)的取值范圍題型九：雙曲線(xiàn)中的范圍與最值問(wèn)題題型十：焦點(diǎn)三角形【知識(shí)點(diǎn)梳理】知識(shí)點(diǎn)一：雙曲線(xiàn)的定義在平面內(nèi)，到兩個(gè)定點(diǎn)SKIPIF1<0、SKIPIF1<0的距離之差的絕對(duì)值等于常數(shù)SKIPIF1<0(SKIPIF1<0大于0且SKIPIF1<0)的動(dòng)點(diǎn)SKIPIF1<0的軌跡叫作雙曲線(xiàn)．這兩個(gè)定點(diǎn)SKIPIF1<0、SKIPIF1<0叫雙曲線(xiàn)的焦點(diǎn)，兩焦點(diǎn)的距離叫作雙曲線(xiàn)的焦距．知識(shí)點(diǎn)詮釋?zhuān)?、雙曲線(xiàn)的定義中，常數(shù)SKIPIF1<0應(yīng)當(dāng)滿(mǎn)足的約束條件：SKIPIF1<0，這可以借助于三角形中邊的相關(guān)性質(zhì)“兩邊之差小于第三邊”來(lái)理解；2、若去掉定義中的“絕對(duì)值”，常數(shù)SKIPIF1<0滿(mǎn)足約束條件：SKIPIF1<0(SKIPIF1<0)，則動(dòng)點(diǎn)軌跡僅表示雙曲線(xiàn)中靠焦點(diǎn)SKIPIF1<0的一支；若SKIPIF1<0(SKIPIF1<0)，則動(dòng)點(diǎn)軌跡僅表示雙曲線(xiàn)中靠焦點(diǎn)SKIPIF1<0的一支；3、若常數(shù)SKIPIF1<0滿(mǎn)足約束條件：SKIPIF1<0，則動(dòng)點(diǎn)軌跡是以F1、F2為端點(diǎn)的兩條射線(xiàn)(包括端點(diǎn))；4、若常數(shù)SKIPIF1<0滿(mǎn)足約束條件：SKIPIF1<0，則動(dòng)點(diǎn)軌跡不存在；5、若常數(shù)SKIPIF1<0，則動(dòng)點(diǎn)軌跡為線(xiàn)段F1F2的垂直平分線(xiàn)．知識(shí)點(diǎn)二：雙曲線(xiàn)的標(biāo)準(zhǔn)方程1、當(dāng)焦點(diǎn)在SKIPIF1<0軸上時(shí)，雙曲線(xiàn)的標(biāo)準(zhǔn)方程：SKIPIF1<0SKIPIF1<0，其中SKIPIF1<0；2、當(dāng)焦點(diǎn)在SKIPIF1<0軸上時(shí)，雙曲線(xiàn)的標(biāo)準(zhǔn)方程：SKIPIF1<0SKIPIF1<0，其中SKIPIF1<0橢圓、雙曲線(xiàn)的區(qū)別和聯(lián)系：橢圓雙曲線(xiàn)根據(jù)|MF1|+|MF2|=2a根據(jù)|MF1|－|MF2|=±2aa＞c＞0，a2－c2=b2(b＞0)0＜a＜c，c2－a2=b2(b＞0)SKIPIF1<0，SKIPIF1<0(a＞b＞0)SKIPIF1<0，SKIPIF1<0(a＞0，b＞0，a不一定大于b)SKIPIF1<0(a最大)SKIPIF1<0(c最大)標(biāo)準(zhǔn)方程統(tǒng)一為：SKIPIF1<0方程Ax2+By2=C(A、B、C均不為零)表示雙曲線(xiàn)的條件方程Ax2+By2=C可化為SKIPIF1<0，即SKIPIF1<0，所以只有A、B異號(hào)，方程表示雙曲線(xiàn)．當(dāng)SKIPIF1<0時(shí)，雙曲線(xiàn)的焦點(diǎn)在x軸上；當(dāng)SKIPIF1<0時(shí)，雙曲線(xiàn)的焦點(diǎn)在y軸上．知識(shí)點(diǎn)詮釋?zhuān)?、當(dāng)且僅當(dāng)雙曲線(xiàn)的對(duì)稱(chēng)中心在坐標(biāo)原點(diǎn)，對(duì)稱(chēng)軸是坐標(biāo)軸，雙曲線(xiàn)的方程才是標(biāo)準(zhǔn)方程形式．此時(shí)，雙曲線(xiàn)的焦點(diǎn)在坐標(biāo)軸上．4、雙曲線(xiàn)標(biāo)準(zhǔn)方程中，a、b、c三個(gè)量的大小與坐標(biāo)系無(wú)關(guān)，是由雙曲線(xiàn)本身所確定的，分別表示雙曲線(xiàn)的實(shí)半軸長(zhǎng)、虛半軸長(zhǎng)和半焦距長(zhǎng)，均為正數(shù)，且三個(gè)量的大小關(guān)系為：c＞a，c＞b，且c2=b2+a2．5、雙曲線(xiàn)的焦點(diǎn)總在實(shí)軸上，因此已知標(biāo)準(zhǔn)方程，判斷焦點(diǎn)位置的方法是：看x2、y2的系數(shù)，如果x2項(xiàng)的系數(shù)是正的，那么焦點(diǎn)在x軸上；如果y2項(xiàng)的系數(shù)是正的，那么焦點(diǎn)在y軸上．6、對(duì)于雙曲線(xiàn)，a不一定大于b，因此不能像橢圓那樣通過(guò)比較分母的大小來(lái)判定焦點(diǎn)在哪一條坐標(biāo)軸上．知識(shí)點(diǎn)三：求雙曲線(xiàn)的標(biāo)準(zhǔn)方程①待定系數(shù)法：由題目條件確定焦點(diǎn)的位置，從而確定方程的類(lèi)型，設(shè)出標(biāo)準(zhǔn)方程，再由條件確定方程中的參數(shù)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的值．其主要步驟是“先定型，再定量”；②定義法：由題目條件判斷出動(dòng)點(diǎn)的軌跡是什么圖形，然后再根據(jù)定義確定方程．知識(shí)點(diǎn)四：雙曲線(xiàn)的簡(jiǎn)單幾何性質(zhì)雙曲線(xiàn)SKIPIF1<0(a＞0，b＞0)的簡(jiǎn)單幾何性質(zhì)范圍SKIPIF1<0雙曲線(xiàn)上所有的點(diǎn)都在兩條平行直線(xiàn)x=-a和x=a的兩側(cè)，是無(wú)限延伸的．因此雙曲線(xiàn)上點(diǎn)的橫坐標(biāo)滿(mǎn)足x≤-a或x≥a．對(duì)稱(chēng)性對(duì)于雙曲線(xiàn)標(biāo)準(zhǔn)方程SKIPIF1<0(a＞0，b＞0)，把x換成-x，或把y換成-y，或把x、y同時(shí)換成-x、-y，方程都不變，所以雙曲線(xiàn)SKIPIF1<0(a＞0，b＞0)是以x軸、y軸為對(duì)稱(chēng)軸的軸對(duì)稱(chēng)圖形，且是以原點(diǎn)為對(duì)稱(chēng)中心的中心對(duì)稱(chēng)圖形，這個(gè)對(duì)稱(chēng)中心稱(chēng)為雙曲線(xiàn)的中心．頂點(diǎn)①雙曲線(xiàn)與它的對(duì)稱(chēng)軸的交點(diǎn)稱(chēng)為雙曲線(xiàn)的頂點(diǎn)．②雙曲線(xiàn)SKIPIF1<0(a＞0，b＞0)與坐標(biāo)軸的兩個(gè)交點(diǎn)即為雙曲線(xiàn)的兩個(gè)頂點(diǎn)，坐標(biāo)分別為A1(-a，0)，A2(a，0)，頂點(diǎn)是雙曲線(xiàn)兩支上的點(diǎn)中距離最近的點(diǎn)．③兩個(gè)頂點(diǎn)間的線(xiàn)段A1A2叫作雙曲線(xiàn)的實(shí)軸；設(shè)B1(0，-b)，B2(0，b)為y軸上的兩個(gè)點(diǎn)，則線(xiàn)段B1B2叫做雙曲線(xiàn)的虛軸．實(shí)軸和虛軸的長(zhǎng)度分別為|A1A2|=2a，|B1B2|=2b．a(chǎn)叫做雙曲線(xiàn)的實(shí)半軸長(zhǎng)，b叫做雙曲線(xiàn)的虛半軸長(zhǎng)．①雙曲線(xiàn)只有兩個(gè)頂點(diǎn)，而橢圓有四個(gè)頂點(diǎn)，不能把雙曲線(xiàn)的虛軸與橢圓的短軸混淆．②雙曲線(xiàn)的焦點(diǎn)總在實(shí)軸上．③實(shí)軸和虛軸等長(zhǎng)的雙曲線(xiàn)稱(chēng)為等軸雙曲線(xiàn)．離心率①雙曲線(xiàn)的焦距與實(shí)軸長(zhǎng)的比叫做雙曲線(xiàn)的離心率，用e表示，記作SKIPIF1<0．②因?yàn)閏＞a＞0，所以雙曲線(xiàn)的離心率SKIPIF1<0．由c2=a2+b2，可得SKIPIF1<0，所以SKIPIF1<0決定雙曲線(xiàn)的開(kāi)口大小，SKIPIF1<0越大，e也越大，雙曲線(xiàn)開(kāi)口就越開(kāi)闊．所以離心率可以用來(lái)表示雙曲線(xiàn)開(kāi)口的大小程度．③等軸雙曲線(xiàn)SKIPIF1<0，所以離心率SKIPIF1<0．漸近線(xiàn)經(jīng)過(guò)點(diǎn)A2、A1作y軸的平行線(xiàn)x=±a，經(jīng)過(guò)點(diǎn)B1、B2作x軸的平行線(xiàn)y=±b，四條直線(xiàn)圍成一個(gè)矩形(如圖)，矩形的兩條對(duì)角線(xiàn)所在直線(xiàn)的方程是SKIPIF1<0．我們把直線(xiàn)SKIPIF1<0叫做雙曲線(xiàn)的漸近線(xiàn)；雙曲線(xiàn)與它的漸近線(xiàn)無(wú)限接近，但永不相交．知識(shí)點(diǎn)四：雙曲線(xiàn)兩個(gè)標(biāo)準(zhǔn)方程幾何性質(zhì)的比較標(biāo)準(zhǔn)方程SKIPIF1<0SKIPIF1<0SKIPIF1<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(chēng)性關(guān)于x軸、y軸和原點(diǎn)對(duì)稱(chēng)頂點(diǎn)SKIPIF1<0SKIPIF1<0軸實(shí)軸長(zhǎng)=SKIPIF1<0，虛軸長(zhǎng)=SKIPIF1<0離心率SKIPIF1<0漸近線(xiàn)方程SKIPIF1<0SKIPIF1<0知識(shí)點(diǎn)詮釋?zhuān)弘p曲線(xiàn)的焦點(diǎn)總在實(shí)軸上，因此已知標(biāo)準(zhǔn)方程，判斷焦點(diǎn)位置的方法是：看x2、y2的系數(shù)，如果x2項(xiàng)的系數(shù)是正的，那么焦點(diǎn)在x軸上；如果y2項(xiàng)的系數(shù)是正的，那么焦點(diǎn)在y軸上．對(duì)于雙曲線(xiàn)，a不一定大于b，因此不能像橢圓那樣通過(guò)比較分母的大小來(lái)判定焦點(diǎn)在哪一條坐標(biāo)軸上．知識(shí)點(diǎn)五：雙曲線(xiàn)的漸近線(xiàn)(1)已知雙曲線(xiàn)方程求漸近線(xiàn)方程：若雙曲線(xiàn)方程為SKIPIF1<0，則其漸近線(xiàn)方程為SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0已知雙曲線(xiàn)方程，將雙曲線(xiàn)方程中的“常數(shù)”換成“0”，然后因式分解即得漸近線(xiàn)方程．(2)已知漸近線(xiàn)方程求雙曲線(xiàn)方程：若雙曲線(xiàn)漸近線(xiàn)方程為SKIPIF1<0，則可設(shè)雙曲線(xiàn)方程為SKIPIF1<0，根據(jù)已知條件，求出SKIPIF1<0即可．(3)與雙曲線(xiàn)SKIPIF1<0有公共漸近線(xiàn)的雙曲線(xiàn)與雙曲線(xiàn)SKIPIF1<0有公共漸近線(xiàn)的雙曲線(xiàn)方程可設(shè)為SKIPIF1<0(SKIPIF1<0，焦點(diǎn)在SKIPIF1<0軸上，SKIPIF1<0，焦點(diǎn)在y軸上)(4)等軸雙曲線(xiàn)的漸近線(xiàn)等軸雙曲線(xiàn)的兩條漸近線(xiàn)互相垂直，為SKIPIF1<0，因此等軸雙曲線(xiàn)可設(shè)為SKIPIF1<0．知識(shí)點(diǎn)六：雙曲線(xiàn)中a，b，c的幾何意義及有關(guān)線(xiàn)段的幾何特征：雙曲線(xiàn)標(biāo)準(zhǔn)方程中，a、b、c三個(gè)量的大小與坐標(biāo)系無(wú)關(guān)，是由雙曲線(xiàn)本身的形狀大小所確定的，分別表示雙曲線(xiàn)的實(shí)半軸長(zhǎng)、虛半軸長(zhǎng)和半焦距長(zhǎng)，均為正數(shù)，且三個(gè)量的大小關(guān)系為：c＞b＞0，c＞a＞0，且c2=b2+a2．雙曲線(xiàn)SKIPIF1<0SKIPIF1<0，如圖：(1)實(shí)軸長(zhǎng)SKIPIF1<0，虛軸長(zhǎng)SKIPIF1<0，焦距SKIPIF1<0(2)離心率：SKIPIF1<0；(3)頂點(diǎn)到焦點(diǎn)的距離：SKIPIF1<0SKIPIF1<0，SKIPIF1<0SKIPIF1<0；【典例例題】題型一：雙曲線(xiàn)的定義、條件例1．平面內(nèi)到兩個(gè)定點(diǎn)SKIPIF1<0的距離之差的絕對(duì)值等于SKIPIF1<0的點(diǎn)的軌跡是(

)A．雙曲線(xiàn) B．兩條射線(xiàn) C．一條線(xiàn)段 D．一條直線(xiàn)例2．到兩定點(diǎn)SKIPIF1<0、SKIPIF1<0的距離之差的絕對(duì)值等于6的點(diǎn)SKIPIF1<0的軌跡(

)A．橢圓 B．直線(xiàn) C．雙曲線(xiàn) D．兩條射線(xiàn)例3．已知?jiǎng)狱c(diǎn)SKIPIF1<0滿(mǎn)足SKIPIF1<0SKIPIF1<0，則動(dòng)點(diǎn)P的軌跡是()A．雙曲線(xiàn) B．雙曲線(xiàn)左支C．雙曲線(xiàn)右支 D．一條射線(xiàn)例4．方程SKIPIF1<0所表示的曲線(xiàn)是(

)A．圓的一部分 B．橢圓的一部分C．雙曲線(xiàn)的一部分 D．直線(xiàn)的一部分例5．在平面直角坐標(biāo)系SKIPIF1<0中，已知點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)Р滿(mǎn)足SKIPIF1<0，則動(dòng)點(diǎn)P的軌跡是(

)A．橢圓 B．拋物線(xiàn)C．雙曲線(xiàn) D．雙曲線(xiàn)的一支題型二：求雙曲線(xiàn)的標(biāo)準(zhǔn)方程例6．求滿(mǎn)足下列條件的雙曲線(xiàn)的標(biāo)準(zhǔn)方程：(1)焦點(diǎn)在SKIPIF1<0軸上，離心率為SKIPIF1<0，兩頂點(diǎn)間的距離為6；(2)以橢圓SKIPIF1<0的焦點(diǎn)為頂點(diǎn)，頂點(diǎn)為焦點(diǎn).例7．求適合下列條件的雙曲線(xiàn)的標(biāo)準(zhǔn)方程：(1)SKIPIF1<0，經(jīng)過(guò)點(diǎn)SKIPIF1<0；(2)焦點(diǎn)SKIPIF1<0軸上，且過(guò)點(diǎn)SKIPIF1<0，SKIPIF1<0.例8．求適合下列條件的雙曲線(xiàn)的標(biāo)準(zhǔn)方程：(1)SKIPIF1<0，SKIPIF1<0，焦點(diǎn)在x軸上；(2)焦點(diǎn)為SKIPIF1<0?SKIPIF1<0，經(jīng)過(guò)點(diǎn)SKIPIF1<0.例9．求適合下列條件的雙曲線(xiàn)的標(biāo)準(zhǔn)方程：(1)焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，且雙曲線(xiàn)上的一點(diǎn)到兩個(gè)焦點(diǎn)距離之差為2；(2)焦點(diǎn)在y軸上，焦距為10，且經(jīng)過(guò)點(diǎn)SKIPIF1<0；(3)經(jīng)過(guò)點(diǎn)SKIPIF1<0，SKIPIF1<0.例10．求適合下列條件的圓錐曲線(xiàn)的標(biāo)準(zhǔn)方程；(1)短軸長(zhǎng)為SKIPIF1<0，離心率SKIPIF1<0的橢圓；(2)與雙曲線(xiàn)SKIPIF1<0具有相同的漸近線(xiàn)，且過(guò)點(diǎn)SKIPIF1<0的雙曲線(xiàn)．題型三：雙曲線(xiàn)的綜合問(wèn)題例11．(多選題)已知雙曲線(xiàn)SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)原點(diǎn)的直線(xiàn)SKIPIF1<0與雙曲線(xiàn)交于A，B兩點(diǎn)，若四邊形SKIPIF1<0為矩形且SKIPIF1<0，則下列正確的是(

)A．SKIPIF1<0 B．E的漸近線(xiàn)方程為SKIPIF1<0C．矩形SKIPIF1<0的面積為SKIPIF1<0 D．E的離心率為SKIPIF1<0例12．(多選題)已知雙曲線(xiàn)SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，點(diǎn)SKIPIF1<0在雙曲線(xiàn)SKIPIF1<0上，下列結(jié)論正確的是(

)A．SKIPIF1<0B．雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)方程為SKIPIF1<0C．存在點(diǎn)SKIPIF1<0，滿(mǎn)足SKIPIF1<0D．點(diǎn)SKIPIF1<0到兩漸近線(xiàn)的距離的乘積為SKIPIF1<0例13．(多選題)雙曲線(xiàn)C：SKIPIF1<0的左右焦點(diǎn)分別是SKIPIF1<0，SKIPIF1<0，左右頂點(diǎn)分別是A，B，兩漸近線(xiàn)分別是SKIPIF1<0，SKIPIF1<0，M在雙曲線(xiàn)C上，其中O是坐標(biāo)原點(diǎn)，則下列說(shuō)法正確的是(

)A．焦點(diǎn)SKIPIF1<0到漸近線(xiàn)SKIPIF1<0的距離是3B．若SKIPIF1<0，則SKIPIF1<0的面積是9C．直線(xiàn)SKIPIF1<0的斜率為SKIPIF1<0，直線(xiàn)SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0D．過(guò)右頂點(diǎn)B作SKIPIF1<0的平行線(xiàn)交SKIPIF1<0于P點(diǎn)，若SKIPIF1<0的面積為3，則雙曲線(xiàn)的離心率為SKIPIF1<0例14．(多選題)已知SKIPIF1<0為坐標(biāo)原點(diǎn)，雙曲線(xiàn)SKIPIF1<0的左焦點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0的一條漸近線(xiàn)的對(duì)稱(chēng)點(diǎn)SKIPIF1<0恰好在SKIPIF1<0上，若直線(xiàn)SKIPIF1<0交SKIPIF1<0的左半支于點(diǎn)SKIPIF1<0，則(

)A．SKIPIF1<0的漸近線(xiàn)方程為SKIPIF1<0 B．SKIPIF1<0的面積為SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0是等腰三角形例15．(多選題)已知SKIPIF1<0、SKIPIF1<0分別是雙曲線(xiàn)SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0上的動(dòng)點(diǎn)，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0到雙曲線(xiàn)SKIPIF1<0一條漸近線(xiàn)的距離為SKIPIF1<0，則下列選項(xiàng)正確的有(

)A．雙曲線(xiàn)SKIPIF1<0的實(shí)軸長(zhǎng)為SKIPIF1<0 B．雙曲線(xiàn)SKIPIF1<0的離心率為SKIPIF1<0C．SKIPIF1<0的最小值為SKIPIF1<0 D．SKIPIF1<0例16．(多選題)已知雙曲線(xiàn)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，點(diǎn)SKIPIF1<0在雙曲線(xiàn)上，則下列結(jié)論正確的是(

)A．該雙曲線(xiàn)的離心率為SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0的面積為SKIPIF1<0C．點(diǎn)SKIPIF1<0到兩漸近線(xiàn)的距離乘積為SKIPIF1<0D．直線(xiàn)SKIPIF1<0和直線(xiàn)SKIPIF1<0的斜率乘積為SKIPIF1<0例17．(多選題)已知曲線(xiàn)SKIPIF1<0分別是曲線(xiàn)C的左、右焦點(diǎn)，則下列說(shuō)法中正確的有(

)A．若SKIPIF1<0，則曲線(xiàn)C的兩條漸近線(xiàn)所成的夾角為SKIPIF1<0B．若曲線(xiàn)C的離心率SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則曲線(xiàn)C上不存在點(diǎn)P使得SKIPIF1<0D．若SKIPIF1<0，P為曲線(xiàn)C上一個(gè)動(dòng)點(diǎn)，則SKIPIF1<0面積的最大值為SKIPIF1<0例18．(多選題)若SKIPIF1<0是橢圓SKIPIF1<0與雙曲線(xiàn)SKIPIF1<0在第一象限的交點(diǎn)，且SKIPIF1<0，SKIPIF1<0共焦點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的離心率分別為SKIPIF1<0，SKIPIF1<0，則下列結(jié)論中正確的是(

)A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<0的最小值為2題型四：軌跡方程例19．已知點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0滿(mǎn)足條件SKIPIF1<0．則動(dòng)點(diǎn)SKIPIF1<0的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例20．已知SKIPIF1<0，若動(dòng)點(diǎn)P滿(mǎn)足直線(xiàn)SKIPIF1<0與直線(xiàn)SKIPIF1<0的斜率之積為SKIPIF1<0，則動(dòng)點(diǎn)P的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例21．動(dòng)圓P過(guò)定點(diǎn)M(0，2)，且與圓N：SKIPIF1<0相內(nèi)切，則動(dòng)圓圓心P的軌跡方程是(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例22．SKIPIF1<0是一個(gè)動(dòng)點(diǎn)，SKIPIF1<0與直線(xiàn)SKIPIF1<0垂直，垂足SKIPIF1<0位于第一象限，SKIPIF1<0與直線(xiàn)SKIPIF1<0垂直，垂足SKIPIF1<0位于第四象限，若四邊形SKIPIF1<0(SKIPIF1<0為原點(diǎn))的面積為4，則動(dòng)點(diǎn)SKIPIF1<0的軌跡方程是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例23．已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，以C為焦點(diǎn)的橢圓過(guò)A、B兩點(diǎn)，則橢圓的另一個(gè)焦點(diǎn)F的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例24．一動(dòng)圓SKIPIF1<0過(guò)定點(diǎn)SKIPIF1<0，且與已知圓SKIPIF1<0：SKIPIF1<0相切，則動(dòng)圓圓心P的軌跡方程是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例25．已知SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)P滿(mǎn)足SKIPIF1<0，則動(dòng)點(diǎn)P的軌跡方程為(

)．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例26．已知一個(gè)動(dòng)圓P與兩圓SKIPIF1<0和SKIPIF1<0都外切，則動(dòng)圓P圓心的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例27．已知SKIPIF1<0的兩個(gè)頂點(diǎn)A，B的坐標(biāo)分別是SKIPIF1<0、SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0所在直線(xiàn)的斜率之積等于2，則頂點(diǎn)C的軌跡方程是(

)A．SKIPIF1<0(SKIPIF1<0) B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0(SKIPIF1<0)例28．已知SKIPIF1<0是圓SKIPIF1<0上的一動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0，線(xiàn)段SKIPIF1<0的垂直平分線(xiàn)交直線(xiàn)SKIPIF1<0于點(diǎn)SKIPIF1<0，則SKIPIF1<0點(diǎn)的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型五：雙曲線(xiàn)的簡(jiǎn)單幾何性質(zhì)例29．已知SKIPIF1<0是雙曲線(xiàn)SKIPIF1<0的兩個(gè)焦點(diǎn)，若雙曲線(xiàn)的左?右頂點(diǎn)和原點(diǎn)把線(xiàn)段SKIPIF1<0四等分，則該雙曲線(xiàn)的焦距為(

)A．1 B．2 C．3 D．4例30．雙曲線(xiàn)SKIPIF1<0的焦點(diǎn)坐標(biāo)為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例31．已知中心在原點(diǎn)，焦點(diǎn)在y軸上的雙曲線(xiàn)的離心率為SKIPIF1<0，則它的漸近線(xiàn)方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例32．已知雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)方程為SKIPIF1<0，若雙曲線(xiàn)C的焦點(diǎn)到漸近線(xiàn)的距離為12，則雙曲線(xiàn)C的焦距為(

)A．30 B．24 C．15 D．12例33．設(shè)雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)方程為SKIPIF1<0，則此雙曲線(xiàn)的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例34．已知雙曲線(xiàn)SKIPIF1<0：SKIPIF1<0的一個(gè)焦點(diǎn)為SKIPIF1<0，則雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)方程為(

).A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型六：求雙曲線(xiàn)的離心率例35．已知雙曲線(xiàn)SKIPIF1<0的一條漸近線(xiàn)方程為SKIPIF1<0，則雙曲線(xiàn)SKIPIF1<0的離心率為(

)A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例36．與橢圓SKIPIF1<0有公共焦點(diǎn)，且離心率SKIPIF1<0的雙曲線(xiàn)的方程為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例37．已知雙曲線(xiàn)SKIPIF1<0：SKIPIF1<0的一條漸近線(xiàn)過(guò)點(diǎn)SKIPIF1<0，則SKIPIF1<0的離心率是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例38．若直線(xiàn)SKIPIF1<0與雙曲線(xiàn)SKIPIF1<0的一條漸近線(xiàn)平行，則實(shí)數(shù)SKIPIF1<0的值為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例39．設(shè)雙曲線(xiàn)SKIPIF1<0(SKIPIF1<0)的半焦距為c，直線(xiàn)l過(guò)SKIPIF1<0兩點(diǎn)，且原點(diǎn)到直線(xiàn)l的距離為SKIPIF1<0，則雙曲線(xiàn)的離心率(

)A．2 B．SKIPIF1<0 C．2和SKIPIF1<0 D．2和SKIPIF1<0例40．以雙曲線(xiàn)C：SKIPIF1<0的實(shí)軸與虛軸端點(diǎn)為頂點(diǎn)的四邊形各邊中點(diǎn)恰在雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)上，則雙曲線(xiàn)C的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例41．SKIPIF1<0分別為雙曲線(xiàn)SKIPIF1<0的左，右焦點(diǎn)，過(guò)SKIPIF1<0的直線(xiàn)與雙曲線(xiàn)左支交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，以SKIPIF1<0為圓心，SKIPIF1<0為半徑的圓經(jīng)過(guò)點(diǎn)SKIPIF1<0，則SKIPIF1<0的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例42．過(guò)雙曲線(xiàn)SKIPIF1<0的右焦點(diǎn)F作一條漸近線(xiàn)的垂線(xiàn)，垂足為A．若SKIPIF1<0(O為坐標(biāo)原點(diǎn))，則該雙曲線(xiàn)的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<0或2例43．已知雙曲線(xiàn)SKIPIF1<0(SKIPIF1<0)的左右焦點(diǎn)分別是SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0在第一象限且在SKIPIF1<0的漸近線(xiàn)上，SKIPIF1<0是以SKIPIF1<0為斜邊的等腰直角三角形，則雙曲線(xiàn)SKIPIF1<0的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．2例44．若雙曲線(xiàn)SKIPIF1<0與雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)相同，則雙曲線(xiàn)SKIPIF1<0的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例45．若雙曲線(xiàn)SKIPIF1<0的漸近線(xiàn)為SKIPIF1<0，則雙曲線(xiàn)的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例46．已知雙曲線(xiàn)的方程為SKIPIF1<0，且雙曲線(xiàn)的一條漸近線(xiàn)的傾斜角SKIPIF1<0滿(mǎn)足SKIPIF1<0，則該雙曲線(xiàn)的離心率為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型七：求雙曲線(xiàn)離心率的取值范圍例47．雙曲線(xiàn)SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為雙曲線(xiàn)右支上一點(diǎn)，若存在SKIPIF1<0，使得SKIPIF1<0，則雙曲線(xiàn)離心率的取值范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例48．已知A，B為雙曲線(xiàn)E的左，右頂點(diǎn)，點(diǎn)M在E上，SKIPIF1<0為等腰三角形，且頂角為135°，則E的離心率為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例49．已知雙曲線(xiàn)SKIPIF1<0的焦距大于SKIPIF1<0，則該雙曲線(xiàn)離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例50．已知雙曲線(xiàn)SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0在雙曲線(xiàn)的右支上，且SKIPIF1<0，則雙曲線(xiàn)離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例51．已知雙曲線(xiàn)SKIPIF1<0的右頂點(diǎn)到其漸近線(xiàn)的距離不大于SKIPIF1<0，其離心率SKIPIF1<0的取值范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例52．已知點(diǎn)F是雙曲線(xiàn)SKIPIF1<0的左焦點(diǎn)，點(diǎn)SKIPIF1<0是該雙曲線(xiàn)的右頂點(diǎn)，過(guò)SKIPIF1<0且垂直于SKIPIF1<0軸的直線(xiàn)與雙曲線(xiàn)交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是鈍角三角形，則該雙曲線(xiàn)的離心率SKIPIF1<0的取值范圍是(

)A．SKIPIF1<0 B．(1，2)C．SKIPIF1<0 D．SKIPIF1<0例53．已知過(guò)雙曲線(xiàn)SKIPIF1<0右焦點(diǎn)且傾斜角為SKIPIF1<0的直線(xiàn)與雙曲線(xiàn)右支有兩個(gè)交點(diǎn)，則雙曲線(xiàn)的離心率SKIPIF1<0的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例54．若雙曲線(xiàn)SKIPIF1<0(SKIPIF1<0)的右支上到原點(diǎn)和右焦點(diǎn)距離相等的點(diǎn)有兩個(gè)，則雙曲線(xiàn)離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例55．已知雙曲線(xiàn)SKIPIF1<0的右支上恰好有兩點(diǎn)到O(坐標(biāo)原點(diǎn))?F(右焦點(diǎn))的距離相等，則雙曲線(xiàn)的離心率e的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．(1，2) D．SKIPIF1<0例56．若雙曲線(xiàn)SKIPIF1<0上不存在點(diǎn)P使得右焦點(diǎn)F關(guān)于直線(xiàn)OP(O為雙曲線(xiàn)的中心)的對(duì)稱(chēng)點(diǎn)在y軸上，則該雙曲線(xiàn)的焦距與實(shí)軸比值的取值范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例57．若雙曲線(xiàn)SKIPIF1<0與直線(xiàn)SKIPIF1<0沒(méi)有公共點(diǎn)，則該雙曲線(xiàn)的離心率e的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例58．已知雙曲線(xiàn)SKIPIF1<0=1(a>0，b>0)的左?右焦點(diǎn)分別為F1(﹣c，0)，F(xiàn)2(c，0)，點(diǎn)P在雙曲線(xiàn)的右支上，且滿(mǎn)足SKIPIF1<0，則該雙曲線(xiàn)離心率的取值范圍是(

)A．(2，+∞) B．(1，2) C．(1，SKIPIF1<0) D．(2，SKIPIF1<0)例59．設(shè)雙曲線(xiàn)SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0.過(guò)左焦點(diǎn)SKIPIF1<0的直線(xiàn)與雙曲線(xiàn)的左支交于點(diǎn)SKIPIF1<0，交雙曲線(xiàn)的右支于點(diǎn)SKIPIF1<0，若滿(mǎn)足SKIPIF1<0，則該雙曲線(xiàn)的離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例60．若雙曲線(xiàn)SKIPIF1<0上存在四個(gè)點(diǎn)A，B，C，D滿(mǎn)足四邊形SKIPIF1<0是正方形，則雙曲線(xiàn)C的離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例61．過(guò)雙曲線(xiàn)C：SKIPIF1<0(a>0，b>0)的右焦點(diǎn)F引一條漸近線(xiàn)的垂線(xiàn)，與另一條漸近線(xiàn)相交于第二象限，則雙曲線(xiàn)C的離心率的取值范圍是(

)A．(SKIPIF1<0，+∞) B．(SKIPIF1<0，+∞) C．(2，+∞) D．(3，+∞)例62．雙曲線(xiàn)SKIPIF1<0：SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)右焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0傾斜角為SKIPIF1<0的直線(xiàn)與雙曲線(xiàn)右支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則雙曲線(xiàn)離心率的范圍為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例63．雙曲線(xiàn)SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，P，Q是該雙曲線(xiàn)右支上不同的兩點(diǎn)，滿(mǎn)足SKIPIF1<0，則此雙曲線(xiàn)離心率的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型八：由雙曲線(xiàn)離心率求參數(shù)的取值范圍例64．已知SKIPIF1<0，SKIPIF1<0是雙曲線(xiàn)C的兩個(gè)焦點(diǎn)，P為C上一點(diǎn)，且SKIPIF1<0，SKIPIF1<0，若C的離心率為SKIPIF1<0，則SKIPIF1<0的值為_(kāi)_____．例65．設(shè)SKIPIF1<0為實(shí)數(shù)，已知雙曲線(xiàn)SKIPIF1<0的離心率SKIPIF1<0，則SKIPIF1<0的取值范圍為_(kāi)____________例66．焦點(diǎn)在SKIPIF1<0軸上的雙曲線(xiàn)SKIPIF1<0的離心率為SKIPIF1<0，則SKIPIF1<0的值為_(kāi)__________.例67．若雙曲線(xiàn)SKIPIF1<0的離心率不大于SKIPIF1<0，則C的虛軸長(zhǎng)的取值范圍為_(kāi)__________.例68．中心在坐標(biāo)原點(diǎn)，離心率為SKIPIF1<0的雙曲線(xiàn)的焦點(diǎn)在y軸上，則它的漸近線(xiàn)方程為_(kāi)_______.例69．已知雙曲線(xiàn)SKIPIF1<0的離心率為2，則點(diǎn)SKIPIF1<0到SKIPIF1<0的漸近線(xiàn)的距離為_(kāi)_____.例70．設(shè)雙曲線(xiàn)SKIPIF1<0的離心率為SKIPIF1<0，其漸近線(xiàn)與圓SKIPIF1<0相切，則SKIPIF1<0________.題型九：雙曲線(xiàn)中的范圍與最值問(wèn)題例71．已知雙曲線(xiàn)SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0?SKIPIF1<0，SKIPIF1<0為雙曲線(xiàn)右支上一點(diǎn)，點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的最小值為_(kāi)__________.例72．已知雙曲線(xiàn)的方程為SKIPIF1<0，如圖所示，點(diǎn)SKIPIF1<0，SKIPIF1<0是圓SKIPIF1<0上的點(diǎn)，點(diǎn)SKIPIF1<0為其圓心，點(diǎn)SKIPIF1<0在雙曲線(xiàn)的右支上，則SKIPIF1<0的最小值為_(kāi)_____例73．已知SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0的右支上一點(diǎn)，SKIPIF1<0，SKIPIF1<0分別是圓SKIPIF1<0和SKIPIF1<0上的點(diǎn)，則SKIPIF1<0的最大值為_(kāi)_______.例74．若SKIPIF1<0是雙曲線(xiàn)SKIPIF1<0的右支上的一點(diǎn),SKIPIF1<0分別是圓SKIPIF1<0和SKIPIF1<0上的點(diǎn),則SKIPIF1<0的最大值為_(kāi)____________.例75．已知SKIPIF1<0是雙曲線(xiàn)SKIPIF1<0的右焦點(diǎn)，動(dòng)點(diǎn)SKIPIF1<0在雙曲線(xiàn)左支上，SKIPIF1<0為圓SKIPIF1<0上一點(diǎn)，則SKIPIF1<0的最小值為_(kāi)______________.例76．SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0右支上一點(diǎn)，SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0的左焦點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為_(kāi)______.例77．已知雙曲線(xiàn)SKIPIF1<0：SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0是雙曲線(xiàn)SKIPIF1<0的左支上一點(diǎn)，SKIPIF1<0，則SKIPIF1<0周長(zhǎng)最小值為_(kāi)_____．題型十：焦點(diǎn)三角形例78．若直線(xiàn)SKIPIF1<0與雙曲線(xiàn)SKIPIF1<0的左支交于不同的兩點(diǎn)，則SKIPIF1<0的取值范圍為_(kāi)_______.例79．已知點(diǎn)F1，F(xiàn)2分別是雙曲線(xiàn)SKIPIF1<0=1的左、右焦點(diǎn)，若點(diǎn)P是雙曲線(xiàn)左支上的點(diǎn)，且SKIPIF1<0，則△SKIPIF1<0的面積為_(kāi)___.例80．點(diǎn)SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0上的點(diǎn)，SKIPIF1<0、SKIPIF1<0為左、右焦點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的面積是__．例81．已知橢圓C與雙曲線(xiàn)E：SKIPIF1<0有相同的焦點(diǎn)SKIPIF1<0，SKIPIF1<0，點(diǎn)M是橢圓C與雙曲線(xiàn)E的一個(gè)公共點(diǎn)，若SKIPIF1<0，則橢圓C的標(biāo)準(zhǔn)方程為_(kāi)________．例82．已知點(diǎn)SKIPIF1<0分別是雙曲線(xiàn)SKIPIF1<0的下、上焦點(diǎn)，若點(diǎn)SKIPIF1<0是雙曲線(xiàn)下支上的點(diǎn)，且SKIPIF1<0，則SKIPIF1<0的面積為_(kāi)_______.例83．已知SKIPIF1<0，SKIPIF1<0為雙曲線(xiàn)SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)P在雙曲線(xiàn)C上，SKIPIF1<0，則SKIPIF1<0______．例84．已知雙曲線(xiàn)SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，過(guò)左焦點(diǎn)SKIPIF1<0交雙曲線(xiàn)左支于A、B兩點(diǎn)，若SKIPIF1<0則SKIPIF1<0等于________.例85．設(shè)雙曲線(xiàn)SKIPIF1<0的兩個(gè)焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，P為雙曲線(xiàn)上一點(diǎn)，若SKIPIF1<0，則SKIPIF1<0______．【過(guò)關(guān)測(cè)試】一、單選題1．與雙曲線(xiàn)SKIPIF1<0有公共焦點(diǎn)，且長(zhǎng)軸長(zhǎng)為SKIPIF1<0的橢圓方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．與兩圓SKIPIF1<0及SKIPIF1<0都外切的圓的圓心的軌跡為(

)A．橢圓 B．雙曲線(xiàn)的一支 C．拋物線(xiàn) D．圓3．雙曲線(xiàn)SKIPIF1<0和SKIPIF1<0的離心率分別為SKIPIF1<0和SKIPIF1<0，若滿(mǎn)足SKIPIF1<0，則下列說(shuō)法正確是(

)A．SKIPIF1<0的漸近線(xiàn)斜率的絕對(duì)值較大，SKIPIF1<0的開(kāi)口較開(kāi)闊B．SKIPIF1<0的漸近線(xiàn)斜率的絕對(duì)值較大，SKIPIF1<0的開(kāi)口較狹窄C．SKIPIF1<0的漸近線(xiàn)斜率的絕對(duì)值較大，SKIPIF1<0的開(kāi)口較開(kāi)闊D．SKIPIF1<0的漸近線(xiàn)斜率的絕對(duì)值較大，SKIPIF1<0的開(kāi)口較狹窄4．如圖所示，某建筑的屋頂采用雙曲面結(jié)構(gòu)，該建筑屋頂外形弧線(xiàn)可看作是雙曲線(xiàn)上支的部分，其離心率為SKIPIF1<0，上頂點(diǎn)坐標(biāo)為(SKIPIF1<0,SKIPIF1<0)，那么該雙曲線(xiàn)的方程可以為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0滿(mǎn)足條件SKIPIF1<0．則動(dòng)點(diǎn)SKIPIF1<0的軌跡方程為(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．頂點(diǎn)距離為6，漸近線(xiàn)方程是SKIPIF1<0的雙曲線(xiàn)方程是(

)A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知雙曲線(xiàn)SKIPIF1<0上一點(diǎn)SKIPIF1<0到左焦點(diǎn)SKIPIF1<0的距離為10，則SKIPIF1<0的中點(diǎn)SKIPIF1<0到坐標(biāo)原點(diǎn)SKIPIF1<0的距離為(

)A．3或7 B．6或14 C．3 D．78．已知雙曲線(xiàn)SKIPIF1<0，點(diǎn)SKIPIF1<0為其兩個(gè)焦點(diǎn)，點(diǎn)SKIPIF1<0為雙曲線(xiàn)上一點(diǎn)，若SKIPIF1<0，則三角形SKIPIF1<0的面積為(

)A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．已知雙曲線(xiàn)SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0是雙曲線(xiàn)上一點(diǎn)，則(

)A．SKIPIF1<0B．當(dāng)雙曲線(xiàn)SKIPIF1<0為等軸雙曲線(xiàn)時(shí)，焦點(diǎn)坐標(biāo)為SKIPIF1<0C．焦點(diǎn)SKIPIF1<0到雙曲線(xiàn)SKIPIF1<0的一條漸近線(xiàn)的距離是定值2D．若雙曲線(xiàn)SKIPIF1<0的一條漸近線(xiàn)方程是SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0或SKIPIF1<010．下列關(guān)于雙曲線(xiàn)SKIPIF1<0說(shuō)法正確的是(

)A．實(shí)軸長(zhǎng)為6 B．與雙曲線(xiàn)SKIPIF1<0有相同的漸近線(xiàn)C．焦點(diǎn)到漸近線(xiàn)距離為4 D．與橢圓SKIPIF1<0有同樣的焦點(diǎn)11．已知雙曲線(xiàn)SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0