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11 雙曲線中的參數(shù)及范圍問題(原卷版)

專題11雙曲線中的參數(shù)及范圍問題限時(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．已知SKIPIF1<0為焦點(diǎn)在SKIPIF1<0軸上的雙曲線，其離心率為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一動(dòng)點(diǎn)（除頂點(diǎn)），過點(diǎn)SKIPIF1<0的直線SKIPIF1<0，SKIPIF1<0分別經(jīng)過雙曲線的兩個(gè)頂點(diǎn)，已知直線SKIPIF1<0的斜率SKIPIF1<0，則直線SKIPIF1<0的斜率SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知雙曲線C：SKIPIF1<0，P為雙曲線C上的一點(diǎn)，若點(diǎn)P到雙曲線C的兩條漸近線的距離之積為1，則雙曲線的半焦距c的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知點(diǎn)SKIPIF1<0為雙曲線SKIPIF1<0的下焦點(diǎn)，SKIPIF1<0為其上頂點(diǎn)，過SKIPIF1<0作垂直于SKIPIF1<0的實(shí)軸的直線交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為銳角三角形，則SKIPIF1<0的離心率的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．平面直角坐標(biāo)系中，SKIPIF1<0為坐標(biāo)原點(diǎn)，給定兩點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0滿足：SKIPIF1<0其中SKIPIF1<0，且SKIPIF1<0已知點(diǎn)SKIPIF1<0的軌跡與雙曲線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，且以SKIPIF1<0為直徑的圓過原點(diǎn)，若雙曲線的離心率不大于SKIPIF1<0，則雙曲線實(shí)軸長(zhǎng)的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．設(shè)雙曲線SKIPIF1<0的離心率為SKIPIF1<0，A，B是雙曲線C上關(guān)于原點(diǎn)對(duì)稱的兩個(gè)點(diǎn)，M是雙曲線C上異于A，B的動(dòng)點(diǎn)，直線SKIPIF1<0斜率分別SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)SKIPIF1<0是雙曲線上位于第一象限的一點(diǎn)，線段SKIPIF1<0過點(diǎn)SKIPIF1<0且SKIPIF1<0，SKIPIF1<0的平分線與線段SKIPIF1<0交于點(diǎn)SKIPIF1<0，與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）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，點(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0上的任意一點(diǎn)，過點(diǎn)SKIPIF1<0作雙曲線SKIPIF1<0的兩條漸近線的平行線，分別與兩條漸近線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若四邊形SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）的面積為SKIPIF1<0，且SKIPIF1<0，則點(diǎn)SKIPIF1<0的縱坐標(biāo)的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，過SKIPIF1<0的直線與雙曲線C的右支交于A，B兩點(diǎn)，△SKIPIF1<0和△SKIPIF1<0的內(nèi)心分別為M，N，則SKIPIF1<0的取值范圍是（

）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SKIPIF1<0為雙曲線SKIPIF1<0上的動(dòng)點(diǎn)，過SKIPIF1<0作兩漸近線的垂線，垂足分別為SKIPIF1<0，SKIPIF1<0，記線段SKIPIF1<0，SKIPIF1<0的長(zhǎng)分別為SKIPIF1<0，SKIPIF1<0，則（

）A．若SKIPIF1<0，SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的最小值為SKIPIF1<0 D．SKIPIF1<0的最小值為SKIPIF1<010．雙曲線SKIPIF1<0的一條漸近線上的點(diǎn)SKIPIF1<0關(guān)于另一條漸近線的對(duì)稱點(diǎn)恰為右焦點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0是雙曲線上的動(dòng)點(diǎn)，則SKIPIF1<0的值可能為A．4 B．SKIPIF1<0 C．2 D．SKIPIF1<011．已知雙曲線C：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，設(shè)點(diǎn)P為C右支上一點(diǎn)，P點(diǎn)到直線SKIPIF1<0的距離為d，過SKIPIF1<0的直線l與雙曲線C的右支有兩個(gè)交點(diǎn)，則下列說法正確的是（

）A．SKIPIF1<0的最小值為2 B．SKIPIF1<0C．直線l的斜率的取值范圍是SKIPIF1<0 D．SKIPIF1<0的內(nèi)切圓圓心到y(tǒng)軸的距離為112．如圖，已知SKIPIF1<0，SKIPIF1<0分別為雙曲線SKIPIF1<0的左、右焦點(diǎn)，兩條漸近線分別為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0，SKIPIF1<0作SKIPIF1<0的垂線，垂足分別為A，B，若四邊形SKIPIF1<0的面積為8，則以下選項(xiàng)正確的有（

）A．SKIPIF1<0B．若SKIPIF1<0，則雙曲線方程為SKIPIF1<0C．若SKIPIF1<0，則離心率e的范圍SKIPIF1<0D．延長(zhǎng)SKIPIF1<0交SKIPIF1<0于點(diǎn)C，若SKIPIF1<0，則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．已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，以SKIPIF1<0為圓心，SKIPIF1<0的虛半軸長(zhǎng)為半徑的圓與SKIPIF1<0的右支恰有兩個(gè)交點(diǎn)，記為SKIPIF1<0、SKIPIF1<0，若四邊形SKIPIF1<0的周長(zhǎng)為SKIPIF1<0，則SKIPIF1<0的焦距的取值范圍為．14．已知A是拋物線SKIPIF1<0：SKIPIF1<0的準(zhǔn)線上的點(diǎn)，B是x軸上一點(diǎn)，O為原點(diǎn)，直線AB與雙曲線SKIPIF1<0：SKIPIF1<0兩漸近線分別交于不同兩點(diǎn)M，N.若雙曲線SKIPIF1<0的離心率為2，SKIPIF1<0，則SKIPIF1<0的取值范圍為.15．已知SKIPIF1<0、SKIPIF1<0分別為雙曲線SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0為雙曲線右支上一點(diǎn)，滿足SKIPIF1<0，直線SKIPIF1<0與圓SKIPIF1<0有公共點(diǎn)，則雙曲線的離心率的取值范圍是.16．已知雙曲線SKIPIF1<0的左右焦點(diǎn)為SKIPIF1<0、SKIPIF1<0，過左焦點(diǎn)SKIPIF1<0作垂直于SKIPIF1<0軸的直線交雙曲線的兩條漸近線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是鈍角，則雙曲線離心率的取值范圍是.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．雙曲線SKIPIF1<0的左頂點(diǎn)為SKIPIF1<0，焦距為4，過右焦點(diǎn)SKIPIF1<0作垂直于實(shí)軸的直線交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，且SKIPIF1<0是直角三角形．(1)求雙曲線SKIPIF1<0的方程；(2)SKIPIF1<0、SKIPIF1<0是SKIPIF1<0右支上的兩動(dòng)點(diǎn)，設(shè)直線SKIPIF1<0、SKIPIF1<0的斜率分別為SKIPIF1<0、SKIPIF1<0，若SKIPIF1<0，求點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離SKIPIF1<0的取值范圍．18．已知圓SKIPIF1<0，定點(diǎn)SKIPIF1<0，N為圓C上一動(dòng)點(diǎn)，線段MN的中垂線與直線CN交于點(diǎn)P．(1)證明：SKIPIF1<0為定值，并求出點(diǎn)P的軌跡SKIPIF1<0的方程；(2)若曲線SKIPIF1<0上一點(diǎn)Q，點(diǎn)A，B分別為SKIPIF1<0在第一象限上的點(diǎn)與SKIPIF1<0在第四象限上的點(diǎn)，若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0面積的取值范圍．19．已知點(diǎn)SKIPIF1<0分別為雙曲線SKIPIF1<0的左頂點(diǎn)和右焦點(diǎn)，過SKIPIF1<0且垂直于SKIPIF1<0軸的直線與雙曲線第一象限部分交于點(diǎn)SKIPIF1<0，SKIPIF1<0的面積為SKIPIF1<0．(1)求雙曲線SKIPIF1<0的方程；(2)若直線SKIPIF1<0與雙曲線的左、右兩支分別交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，與雙曲線的兩條漸近線分別交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，記SKIPIF1<0，SKIPIF1<0的面積分別為SKIPIF1<0，SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）．若SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍．20．已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與雙曲線SKIPIF1<0的右支相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸對(duì)稱的點(diǎn)為SKIPIF1<0.當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.(1)求雙曲線SKIPIF1<0的方程；(2)若SKIPIF1<0的外心為SKIPIF1<0，求SKIPIF1<0的取值范圍.21．已知拋物線SKIPIF1<0