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14 雙曲線中的向量問題(原卷版)

專題14雙曲線中的向量問題限時(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．若斜率為SKIPIF1<0（SKIPIF1<0）的直線SKIPIF1<0過雙曲線SKIPIF1<0：SKIPIF1<0的上焦點(diǎn)SKIPIF1<0，與雙曲線SKIPIF1<0的上支交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知雙曲線SKIPIF1<0的右頂點(diǎn)?右焦點(diǎn)分別為A，F(xiàn)，過點(diǎn)A的直線l與C的一條漸近線交于點(diǎn)Q，直線SKIPIF1<0與C的一個(gè)交點(diǎn)為B，若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知點(diǎn)P為雙曲線C：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）上位于第一象限內(nèi)的一點(diǎn)，過點(diǎn)P向雙曲線C的一條漸近線l作垂線，垂足為A，SKIPIF1<0為雙曲線C的左焦點(diǎn)，若SKIPIF1<0，則漸近線l的斜率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知雙曲線SKIPIF1<0右支上的一點(diǎn)P，經(jīng)過點(diǎn)P的直線與雙曲線C的兩條漸近線分別相交于A，B兩點(diǎn)．若點(diǎn)A，B分別位于第一、四象限，O為坐標(biāo)原點(diǎn)．當(dāng)點(diǎn)P為AB的中點(diǎn)時(shí)，SKIPIF1<0（

）A．SKIPIF1<0 B．9 C．SKIPIF1<0 D．SKIPIF1<05．過雙曲線SKIPIF1<0的右焦點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線分別交雙曲線的漸近線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0在第一象限，SKIPIF1<0在第二象限，若SKIPIF1<0，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．26．已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，過SKIPIF1<0的直線SKIPIF1<0交雙曲線的右支于SKIPIF1<0、SKIPIF1<0兩點(diǎn)．點(diǎn)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，者SKIPIF1<0，則雙曲線的離心率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，過SKIPIF1<0的左頂點(diǎn)SKIPIF1<0作一條與漸近線平行的直線與SKIPIF1<0軸相交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0為線段SKIPIF1<0上一個(gè)動點(diǎn)，當(dāng)SKIPIF1<0分別取得最小值和最大值時(shí)，點(diǎn)SKIPIF1<0的縱坐標(biāo)分別記為SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知橢圓SKIPIF1<0與雙曲線SKIPIF1<0有相同的左焦點(diǎn)SKIPIF1<0、右焦點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0是兩曲線的一個(gè)交點(diǎn)，且SKIPIF1<0.過SKIPIF1<0作傾斜角為45°的直線交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)（點(diǎn)SKIPIF1<0在SKIPIF1<0軸的上方），且SKIPIF1<0，則SKIPIF1<0的值為（

）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：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且C的一條漸近線經(jīng)過點(diǎn)SKIPIF1<0，直線SKIPIF1<0與C的另一條漸近線在第四象限交于點(diǎn)A，則下列結(jié)論正確的是（

）A．C的離心率為2B．若SKIPIF1<0，則C的方程為SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0（O為坐標(biāo)原點(diǎn)）的面積為SKIPIF1<0D．若SKIPIF1<0，則C的焦距為SKIPIF1<010．已知雙曲線SKIPIF1<0，SKIPIF1<0，O為坐標(biāo)原點(diǎn)，M為雙曲線上任意一點(diǎn)，則SKIPIF1<0的值可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知雙曲線SKIPIF1<0的右頂點(diǎn)、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0的一條漸近線交于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與SKIPIF1<0的一個(gè)交點(diǎn)為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則下列結(jié)論正確的是（

）A．直線SKIPIF1<0與SKIPIF1<0軸垂直 B．SKIPIF1<0的離心率為SKIPIF1<0C．SKIPIF1<0的漸近線方程為SKIPIF1<0 D．SKIPIF1<0（其中SKIPIF1<0為坐標(biāo)原點(diǎn)）12．已知雙曲線SKIPIF1<0且SKIPIF1<0成等差數(shù)列，過雙曲線的右焦點(diǎn)F（c，0）的直線l與雙曲線C的右支相交于A，B兩點(diǎn)，SKIPIF1<0，則直線l的斜率的可能取值為（

）A．SKIPIF1<0 B．－SKIPIF1<0 C．SKIPIF1<0 D．－SKIPIF1<0三、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．設(shè)雙曲線C的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且焦距為SKIPIF1<0，P是C上一點(diǎn)，滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的周長為．14．已知SKIPIF1<0，點(diǎn)P滿足SKIPIF1<0，動點(diǎn)M，N滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值是．15．已知雙曲線SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0?SKIPIF1<0，實(shí)軸長為1，SKIPIF1<0是雙曲線右支上的一點(diǎn)，滿足SKIPIF1<0，SKIPIF1<0是SKIPIF1<0軸上的一點(diǎn)，則SKIPIF1<0.16．設(shè)雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，過SKIPIF1<0的直線SKIPIF1<0與雙曲線的左?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)寫出必要的文字說明、證明過程或演算步驟．17．已知雙曲線C的漸近線為SKIPIF1<0，右焦點(diǎn)為SKIPIF1<0，右頂點(diǎn)為A.(1)求雙曲線C的標(biāo)準(zhǔn)方程；(2)若斜率為1的直線l與雙曲線C交于M，N兩點(diǎn)（與點(diǎn)A不重合），當(dāng)SKIPIF1<0時(shí)，求直線l的方程.18．已知SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0，記點(diǎn)SKIPIF1<0的軌跡為SKIPIF1<0，(1)求軌跡SKIPIF1<0的方程；(2)若直線SKIPIF1<0過點(diǎn)SKIPIF1<0，且與軌跡SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)．在SKIPIF1<0軸上是否存在定點(diǎn)SKIPIF1<0，無論直線SKIPIF1<0繞點(diǎn)SKIPIF1<0怎樣轉(zhuǎn)動，使SKIPIF1<0恒成立？如果存在，求出定點(diǎn)SKIPIF1<0；如果不存在，請說明理由．19．已知雙曲線C：SKIPIF1<0，直線l在x軸上方與x軸平行，交雙曲線C于A，B兩點(diǎn)，直線l交y軸于點(diǎn)D.當(dāng)l經(jīng)過C的焦點(diǎn)時(shí)，點(diǎn)A的坐標(biāo)為SKIPIF1<0.(1)求C的方程；(2)設(shè)OD的中點(diǎn)為M，是否存在定直線l，使得經(jīng)過M的直線與C交于P，Q，與線段AB交于點(diǎn)N，SKIPIF1<0，SKIPIF1<0均成立；若存在，求出l的方程；若不存在，請說明理由.20．已知雙曲線SKIPIF1<0的虛軸長為SKIPIF1<0，左焦點(diǎn)為F．(1)設(shè)O為坐標(biāo)原點(diǎn)，若過F的直線l與C的兩條漸近線分別交于A，B兩點(diǎn)，當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的面積；(2)設(shè)過F的直線l與C交于M，N兩點(diǎn)，若x軸上存在一點(diǎn)P，使得SKIPIF1<0為定值，求出點(diǎn)P的坐標(biāo)及該定值．21．點(diǎn)SKIPIF1<0在以SKIPIF1<0、SKIPIF1<0為焦點(diǎn)的雙曲線SKIPIF1<0上，已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)．(1)求雙曲線的離心率SKIPIF1<0；(2)過點(diǎn)SKIPIF1<0作直線分別與雙曲線漸近線相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，且SKIPIF1<0