新高考數(shù)學(xué)一輪復(fù)習(xí) 圓錐曲線專項(xiàng)重難點(diǎn)突破專題10 雙曲線中的最值問(wèn)題(原卷版)

專題10雙曲線中的最值問(wèn)題限時(shí)：120分鐘滿分：150分一、單選題：本大題共8小題，每個(gè)小題5分，共40分.在每小題給出的選項(xiàng)中，只有一項(xiàng)是符合題目要求的.1．已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，動(dòng)點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0的右支上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．過(guò)橢圓SKIPIF1<0右焦點(diǎn)F的圓與圓SKIPIF1<0外切，該圓直徑SKIPIF1<0的端點(diǎn)Q的軌跡記為曲線C，若P為曲線C上的一動(dòng)點(diǎn)，則SKIPIF1<0長(zhǎng)度最小值為（

）A．0 B．SKIPIF1<0 C．1 D．23．已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0的左支上，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0的一條漸近線的垂線，垂足為SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知點(diǎn)A在雙曲線C：SKIPIF1<0（b>0）上，且雙曲線C的上?下焦點(diǎn)分別為F1，F(xiàn)2，點(diǎn)B在∠F1AF2的平分線上，BF2⊥AB，若點(diǎn)D在直線l：SKIPIF1<0，則|BD|的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知雙曲線SKIPIF1<0的右焦點(diǎn)為F，SKIPIF1<0，直線MF與y軸交于點(diǎn)N，點(diǎn)P為雙曲線上一動(dòng)點(diǎn)，且SKIPIF1<0，直線MP與以MN為直徑的圓交于點(diǎn)M?Q，則SKIPIF1<0的最大值為（

）A．48 B．49 C．50 D．426．已知直線SKIPIF1<0與雙曲線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．20 B．22 C．24 D．257．雙曲線SKIPIF1<0右焦點(diǎn)為SKIPIF1<0，離心率為SKIPIF1<0，SKIPIF1<0，以SKIPIF1<0為圓心，SKIPIF1<0長(zhǎng)為半徑的圓與雙曲線有公共點(diǎn)，則SKIPIF1<0最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．設(shè)雙曲線SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，過(guò)SKIPIF1<0左焦點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線SKIPIF1<0依次交SKIPIF1<0的左右兩支于SKIPIF1<0，SKIPIF1<0，則有SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的中點(diǎn)，則直線SKIPIF1<0斜率的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題：本大題共4小題，每個(gè)小題5分，共20分.在每小題給出的選項(xiàng)中，只有一項(xiàng)或者多項(xiàng)是符合題目要求的.9．已知雙曲線C的方程為SKIPIF1<0，則下列說(shuō)法正確的是（

）A．雙曲線C的漸近線方程為SKIPIF1<0B．雙曲線C的實(shí)軸長(zhǎng)為8C．雙曲線C的焦點(diǎn)到漸近線的距離為3D．雙曲線C上的點(diǎn)到焦點(diǎn)的距離的最小值為SKIPIF1<010．已知雙曲線SKIPIF1<0，過(guò)其右焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0與雙曲線交于兩點(diǎn)SKIPIF1<0，SKIPIF1<0，則（

）A．若SKIPIF1<0在雙曲線右支上，則SKIPIF1<0的最短長(zhǎng)度為1B．若SKIPIF1<0，SKIPIF1<0同在雙曲線右支上，則SKIPIF1<0的斜率大于SKIPIF1<0C．SKIPIF1<0的最短長(zhǎng)度為6D．滿足SKIPIF1<0的直線SKIPIF1<0有4條11．已知SKIPIF1<0為坐標(biāo)原點(diǎn)，雙曲線SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，離心率為2，過(guò)SKIPIF1<0的直線與雙曲線的右支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0的最小值為6，則（

）A．該雙曲線的方程為SKIPIF1<0 B．若SKIPIF1<0，則直線SKIPIF1<0的斜率為SKIPIF1<0C．SKIPIF1<0的最小值為25 D．SKIPIF1<0面積的最小值為1212．已知?jiǎng)狱c(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0上的點(diǎn)，點(diǎn)SKIPIF1<0是SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0是雙曲線SKIPIF1<0的左、右頂點(diǎn)，下列結(jié)論正確的是（）A．雙曲線SKIPIF1<0的離心率為SKIPIF1<0B．點(diǎn)SKIPIF1<0在雙曲線的左支時(shí)，SKIPIF1<0的最大值為SKIPIF1<0C．點(diǎn)SKIPIF1<0到兩漸近線的距離之積為定值D．若SKIPIF1<0是△SKIPIF1<0的面積，則SKIPIF1<0為定值三、填空題：本大題共4小題，每小題5分，共20分.把答案填在答題卡中的橫線上.13．已知雙曲線C的方程為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，雙曲線C上存在一點(diǎn)P，使得SKIPIF1<0，則實(shí)數(shù)a的最大值為.14．雙曲線SKIPIF1<0：SKIPIF1<0的左，右頂點(diǎn)分別是SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0上任意一點(diǎn)，直線SKIPIF1<0，SKIPIF1<0分別與直線SKIPIF1<0：SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值是．15．已知點(diǎn)SKIPIF1<0，若雙曲線SKIPIF1<0的右支上存在兩動(dòng)點(diǎn)SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的最小值為.16．已知雙曲線SKIPIF1<0，過(guò)雙曲線C上任意一點(diǎn)P作兩條漸近線的垂線，垂足分別為M，N，則SKIPIF1<0的最小值為.四、解答題：本大題共6小題，共70分.解答應(yīng)寫出必要的文字說(shuō)明、證明過(guò)程或演算步驟．17．已知雙曲線SKIPIF1<0的實(shí)軸長(zhǎng)為SKIPIF1<0，離心率為SKIPIF1<0.動(dòng)點(diǎn)P是雙曲線C上任意一點(diǎn).(1)求雙曲線C的標(biāo)準(zhǔn)方程；(2)已知點(diǎn)SKIPIF1<0，求線段SKIPIF1<0的中點(diǎn)Q的軌跡方程；(3)已知點(diǎn)SKIPIF1<0，求SKIPIF1<0的最小值.18．在平面內(nèi)，動(dòng)點(diǎn)M（x，y）與定點(diǎn)F（2，0）的距離和它到定直線SKIPIF1<0的距離比是常數(shù)2.(1)求動(dòng)點(diǎn)SKIPIF1<0的軌跡方程；(2)若直線SKIPIF1<0與動(dòng)點(diǎn)SKIPIF1<0的軌跡交于P，Q兩點(diǎn)，且SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），求SKIPIF1<0的最小值.19．已知雙曲線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，左?右頂點(diǎn)分別是SKIPIF1<0，右焦點(diǎn)SKIPIF1<0到漸近線的距離為SKIPIF1<0，動(dòng)直線SKIPIF1<0與以SKIPIF1<0為直徑的圓相切，且SKIPIF1<0與SKIPIF1<0的左?右兩支分別交于SKIPIF1<0兩點(diǎn).(1)求雙曲線C的方程；(2)記直線SKIPIF1<0的斜率分別為SKIPIF1<0，求SKIPIF1<0的最小值.20．設(shè)雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且E的漸近線方程為SKIPIF1<0．(1)求E的方程；(2)過(guò)SKIPIF1<0作兩條相互垂直的直線SKIPIF1<0和SKIPIF1<0，與E的右支分別交于A，C兩點(diǎn)和B，D兩點(diǎn)，求四邊形ABCD面積的最小值．21．已知雙曲線SKIPIF1<0，（SKIPIF1<0，SKIPIF1<0）的實(shí)軸長(zhǎng)為2，且過(guò)點(diǎn)SKIPIF1<0，其中