新高考數(shù)學(xué)二輪復(fù)習(xí)培優(yōu)專題15 圓錐曲線綜合問題（單選+填空）（原卷版）

試卷第=page11頁，共=sectionpages33頁專題15圓錐曲線綜合問題（單選+填空）一、單選題1．（2023·江蘇南通·統(tǒng)考模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線上，且SKIPIF1<0，若SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0（

）A．2 B．4 C．SKIPIF1<0 D．SKIPIF1<02．（2023秋·浙江紹興·高三統(tǒng)考期末）若橢圓SKIPIF1<0的左焦點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0對稱的點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，則橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023春·湖南長沙·高三長郡中學(xué)?？茧A段練習(xí)）已知SKIPIF1<0，SKIPIF1<0是雙曲線SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0的離心率為SKIPIF1<0，則SKIPIF1<0的值為（

）A．3 B．SKIPIF1<0 C．2 D．SKIPIF1<04．（2023春·湖北·高三統(tǒng)考階段練習(xí)）如圖所示，SKIPIF1<0，SKIPIF1<0是雙曲線SKIPIF1<0的左、右焦點(diǎn)，雙曲線SKIPIF1<0的右支上存在一點(diǎn)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0與雙曲線SKIPIF1<0的左支的交點(diǎn)A平分線段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．（2023秋·江蘇無錫·高三統(tǒng)考期末）雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0的直線與雙曲線左、右兩支分別交于點(diǎn)P，Q，若SKIPIF1<0，M為PQ的中點(diǎn)，且SKIPIF1<0，則雙曲線的離心率為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．26．（2023秋·江蘇蘇州·高三統(tǒng)考期末）在平面直角坐標(biāo)系SKIPIF1<0中，已知雙曲線C：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的左頂點(diǎn)為SKIPIF1<0，右焦點(diǎn)為F，過點(diǎn)F作C的一條漸近線的垂線，垂足為P，過點(diǎn)P作x軸的垂線，垂足為Q．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等差數(shù)列，則C的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<07．（2023·山東日照·統(tǒng)考一模）已知橢圓SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0內(nèi)一點(diǎn)，點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0：SKIPIF1<0上，若橢圓上存在一點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023·山東威?！そy(tǒng)考一模）已知雙曲線SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，M為C上一點(diǎn)，M關(guān)于原點(diǎn)的對稱點(diǎn)為N，若SKIPIF1<0，且SKIPIF1<0，則C的漸近線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023春·湖北·高三統(tǒng)考階段練習(xí)）已知雙曲線SKIPIF1<0為雙曲線的右焦點(diǎn)，過點(diǎn)SKIPIF1<0作漸近線的垂線SKIPIF1<0，垂足為SKIPIF1<0，交另一條漸近線于SKIPIF1<0，若SKIPIF1<0，則雙曲線SKIPIF1<0的離心率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．（2023·湖南邵陽·統(tǒng)考二模）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，半焦距為SKIPIF1<0．在橢圓上存在點(diǎn)SKIPIF1<0使得SKIPIF1<0，則橢圓離心率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2023·江蘇南通·校聯(lián)考模擬預(yù)測）如圖1所示，拋物面天線是指由拋物面（拋物線繞其對稱軸旋轉(zhuǎn)形成的曲面）反射器和位于焦點(diǎn)上的照射器（饋源，通常采用喇叭天線）組成的單反射面型天線，廣泛應(yīng)用于微波和衛(wèi)星通訊等領(lǐng)域，具有結(jié)構(gòu)簡單、方向性強(qiáng)、工作頻帶寬等特點(diǎn)．圖2是圖1的軸截面，A，B兩點(diǎn)關(guān)于拋物線的對稱軸對稱，F(xiàn)是拋物線的焦點(diǎn)，∠AFB是饋源的方向角，記為SKIPIF1<0，焦點(diǎn)F到頂點(diǎn)的距離f與口徑d的比值SKIPIF1<0稱為拋物面天線的焦徑比，它直接影響天線的效率與信噪比等．如果某拋物面天線饋源的方向角SKIPIF1<0滿足，SKIPIF1<0，則其焦徑比為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2023·廣東廣州·統(tǒng)考一模）已知拋物線SKIPIF1<0的頂點(diǎn)為坐標(biāo)原點(diǎn)SKIPIF1<0，焦點(diǎn)SKIPIF1<0在SKIPIF1<0軸上，過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則直線SKIPIF1<0的斜率的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．113．（2023春·廣東珠海·高三珠海市第一中學(xué)?？茧A段練習(xí)）已知點(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0的右焦點(diǎn)，過點(diǎn)F向C的一條漸近線引垂線垂足為A，交另一條漸近線于點(diǎn)B．若SKIPIF1<0，則雙曲線C的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2023·浙江·模擬預(yù)測）已知橢圓SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0為橢圓上一點(diǎn)，過P點(diǎn)作橢圓的切線l，PM垂直于直線l且與x軸交于點(diǎn)M，若M為SKIPIF1<0的中點(diǎn)，則該橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（2023·江蘇宿遷·江蘇省沭陽高級中學(xué)?？寄M預(yù)測）橢圓具有光學(xué)性質(zhì)：從橢圓的一個(gè)焦點(diǎn)發(fā)出的光線，經(jīng)過橢圓反射后，反射光線過橢圓的另一個(gè)焦點(diǎn)(如圖).已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，過SKIPIF1<0的直線與橢圓E交與點(diǎn)A，B，過點(diǎn)A作橢圓的切線l，點(diǎn)B關(guān)于l的對稱點(diǎn)為M，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．（2023春·湖北·高三統(tǒng)考階段練習(xí)）如圖，SKIPIF1<0為雙曲線的左右焦點(diǎn)，過SKIPIF1<0的直線交雙曲線于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為線段的SKIPIF1<0中點(diǎn)，若對于線段SKIPIF1<0上的任意點(diǎn)SKIPIF1<0，都有SKIPIF1<0成立，且SKIPIF1<0內(nèi)切圓的圓心在直線SKIPIF1<0上.則雙曲線的離心率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<017．（2023·湖北·統(tǒng)考模擬預(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的直線分別交雙曲線左、右兩支于A，B兩點(diǎn)，點(diǎn)C在x軸上，SKIPIF1<0，SKIPIF1<0平分SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．（2023春·浙江溫州·高三統(tǒng)考開學(xué)考試）直線l與雙曲線SKIPIF1<0的左，右兩支分別交于點(diǎn)A，B，與雙曲線的兩條漸近線分別交于點(diǎn)C，D（A，C，D，B從左到右依次排列），若SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等差數(shù)列，則雙曲線的離心率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．（2023春·浙江寧波·高三校聯(lián)考階段練習(xí)）已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0為橢圓上不與頂點(diǎn)重合的任意一點(diǎn)，SKIPIF1<0為SKIPIF1<0的內(nèi)心，記直線SKIPIF1<0的斜率分別為SKIPIF1<0，若SKIPIF1<0，則橢圓SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題20．（2023秋·浙江·高三期末）已知橢圓SKIPIF1<0，過橢圓左焦點(diǎn)F任作一條弦SKIPIF1<0（不與長軸重合），點(diǎn)A，B是橢圓的左右頂點(diǎn)，設(shè)直線SKIPIF1<0的斜率為SKIPIF1<0，直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0的最小值為_______．21．（2023·浙江嘉興·統(tǒng)考模擬預(yù)測）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0的直線分別交兩條漸近線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的離心率為______.22．（2023春·江蘇南京·高三南京市第五高級中學(xué)?？茧A段練習(xí)）已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，若以SKIPIF1<0為圓心，b－c為半徑作圓SKIPIF1<0，過橢圓上一點(diǎn)P作此圓的切線．切點(diǎn)為T，且|PT|的最小值為SKIPIF1<0，則橢圓的離心率e的取值范圍是____________．23．（2023·山東泰安·統(tǒng)考一模）已知雙曲線C：SKIPIF1<0的右頂點(diǎn)為A，以A為圓心，b為半徑的圓與雙曲線C的一條漸近線交于M，N兩點(diǎn)，若SKIPIF1<0，則以SKIPIF1<0（e為雙曲線C的離心率）為焦點(diǎn)的拋物線的標(biāo)準(zhǔn)方程為___________.24．（2023春·湖北·高三統(tǒng)考階段練習(xí)）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線與該拋物線交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0的中點(diǎn)縱坐標(biāo)為SKIPIF1<0，則SKIPIF1<0__________.25．（2023·湖北·統(tǒng)考模擬預(yù)測）已知SKIPIF1<0為拋物線SKIPIF1<0上一點(diǎn)，過點(diǎn)SKIPIF1<0的直線與拋物線C交于A，B兩點(diǎn)，且直線SKIPIF1<0與SKIPIF1<0的傾斜角互補(bǔ)，則SKIPIF1<0__________．26．（2023·湖南·湖南師大附中校聯(lián)考模擬預(yù)測）已知直線SKIPIF1<0，拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸對稱的點(diǎn)為SKIPIF1<0.若過點(diǎn)SKIPIF1<0的圓與直線SKIPIF1<0相切，且與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0的斜率為___________.27．（2023秋·湖南湘潭·高三校聯(lián)考期末）已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0