新高考數(shù)學(xué)二輪復(fù)習(xí)強(qiáng)化練習(xí)專題18 圓錐曲線的幾何性質(zhì)問題（練）（原卷版）

第一篇熱點(diǎn)、難點(diǎn)突破篇專題18圓錐曲線的幾何性質(zhì)問題（練）【對點(diǎn)演練】一、單選題1．（2022秋·福建寧德·高三?？计谀┮阎獟佄锞€SKIPIF1<0的焦點(diǎn)為F，拋物線上一點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<02．（2023秋·貴州銅仁·高三統(tǒng)考期末）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上不同兩點(diǎn)，且SKIPIF1<0中點(diǎn)的橫坐標(biāo)為SKIPIF1<0，則SKIPIF1<0（

）A．4 B．5 C．6 D．83．（2023·高三課時(shí)練習(xí)）已知橢圓SKIPIF1<0的左準(zhǔn)線為l，左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，拋物線SKIPIF1<0的準(zhǔn)線也為l，焦點(diǎn)是SKIPIF1<0，SKIPIF1<0與SKIPIF1<0的一個(gè)交點(diǎn)為點(diǎn)P，則SKIPIF1<0的值等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．84．（2023·全國·校聯(lián)考模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，記SKIPIF1<0與SKIPIF1<0的面積分別為SKIPIF1<0和SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022秋·福建寧德·高三?？计谀┮阎p曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，過SKIPIF1<0的直線l交雙曲線于A，B兩點(diǎn)，A，B分別位于第一、第二象限，SKIPIF1<0為等邊三角形，則雙曲線的離心率SKIPIF1<0（

）A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．76．（2023秋·江西撫州·高三臨川一中校考期末）已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，點(diǎn)SKIPIF1<0是雙曲線在第二象限的部分上一點(diǎn)，且SKIPIF1<0，SKIPIF1<0，則雙曲線的離心率為（

）A．3 B．2 C．SKIPIF1<0 D．SKIPIF1<0二、多選題7．（2023秋·江蘇揚(yáng)州·高三校聯(lián)考期末）已知非零常數(shù)a，若點(diǎn)A的坐標(biāo)為SKIPIF1<0，點(diǎn)B的坐標(biāo)為SKIPIF1<0，直線SKIPIF1<0與SKIPIF1<0相交于點(diǎn)P，且它們的斜率之積為非零常數(shù)SKIPIF1<0，那么下列說法中正確的有（

）．A．當(dāng)SKIPIF1<0時(shí)，點(diǎn)P的軌跡加上A，B兩點(diǎn)所形成的曲線是焦點(diǎn)在x軸上的橢圓B．當(dāng)SKIPIF1<0時(shí)，點(diǎn)P的軌跡加上A，B兩點(diǎn)所形成的曲線是圓心在原點(diǎn)的圓C．當(dāng)SKIPIF1<0時(shí)，點(diǎn)P的軌跡加上A，B兩點(diǎn)所形成的曲線是焦點(diǎn)在y軸上的橢圓D．當(dāng)SKIPIF1<0時(shí)，點(diǎn)P的軌跡加上A，B兩點(diǎn)所形成的曲線是焦點(diǎn)在x軸上的雙曲線三、填空題8．（2023·高三課時(shí)練習(xí)）已知雙曲線E：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，點(diǎn)P在雙曲線E上，且SKIPIF1<0，則SKIPIF1<0=______.9．（2022·全國·統(tǒng)考高考真題）記雙曲線SKIPIF1<0的離心率為e，寫出滿足條件“直線SKIPIF1<0與C無公共點(diǎn)”的e的一個(gè)值______________．10．（2022·全國·統(tǒng)考高考真題）若雙曲線SKIPIF1<0的漸近線與圓SKIPIF1<0相切，則SKIPIF1<0_________．【沖刺提升】一、單選題1．（2023秋·江西·高三校聯(lián)考期末）如圖，已知拋物線E：SKIPIF1<0的焦點(diǎn)為F，過F且斜率為1的直線交E于A，B兩點(diǎn)，線段AB的中點(diǎn)為M，其垂直平分線交x軸于點(diǎn)C，SKIPIF1<0軸于點(diǎn)N.若四邊形SKIPIF1<0的面積等于8，則E的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022秋·福建寧德·高三?？计谀┰O(shè)橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上（SKIPIF1<0位于第一象限），且點(diǎn)SKIPIF1<0，SKIPIF1<0關(guān)于原點(diǎn)對稱，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03.（2023秋·貴州銅仁·高三統(tǒng)考期末）已知SKIPIF1<0是雙曲線SKIPIF1<0的左、右焦點(diǎn)，過SKIPIF1<0的直線l與雙曲線的左支交于點(diǎn)A，與右支交于點(diǎn)B，若SKIPIF1<0，且雙曲線的離心率為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2023秋·河北邯鄲·高三統(tǒng)考期末）已知雙曲線SKIPIF1<0的上、下焦點(diǎn)分別為SKIPIF1<0，點(diǎn)P在雙曲線上且位于x軸上方，則下列結(jié)論正確的是（

）A．線段SKIPIF1<0的最小值為1B．點(diǎn)P到兩漸近線的距離的乘積為SKIPIF1<0C．若SKIPIF1<0為直角三角形，則SKIPIF1<0的面積為5D．SKIPIF1<0的內(nèi)切圓圓心在直線SKIPIF1<0上5．（2023秋·山西太原·高三統(tǒng)考期末）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩個(gè)不同點(diǎn)，則下列結(jié)論正確的是（

）A．若點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值是3B．SKIPIF1<0的最小值是2C．若SKIPIF1<0，則直線SKIPIF1<0的斜率為SKIPIF1<0D．過點(diǎn)SKIPIF1<0分別作拋物線SKIPIF1<0的切線，設(shè)兩切線的交點(diǎn)為SKIPIF1<0，則點(diǎn)SKIPIF1<0的橫坐標(biāo)為SKIPIF1<0三、填空題6．（2023·高三課時(shí)練習(xí)）已知SKIPIF1<0、SKIPIF1<0是橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，P為橢圓C上的一點(diǎn)，且SKIPIF1<0，若SKIPIF1<0的面積為9，則b=______．7．（2023·廣西柳州·統(tǒng)考模擬預(yù)測）雙曲線SKIPIF1<0的一條漸近線與曲線SKIPIF1<0交于M、N兩個(gè)不同的點(diǎn)，則SKIPIF1<0__________．8．（2023·高三課時(shí)練習(xí)）設(shè)平面直角坐標(biāo)系中，O為原點(diǎn)，N為動(dòng)點(diǎn)，SKIPIF1<0，SKIPIF1<0，過點(diǎn)M作SKIPIF1<0軸于點(diǎn)SKIPIF1<0，過點(diǎn)N作SKIPIF1<0軸于點(diǎn)SKIPIF1<0，M與SKIPIF1<0不重合，N與SKIPIF1<0不重合，設(shè)SKIPIF1<0，則點(diǎn)T的軌跡方程是______.9．（2023秋·海南·高三統(tǒng)考期末）如圖，已知SKIPIF1<0，SKIPIF1<0分別是橢圓SKIPIF1<0的左、右焦點(diǎn)，M，N為橢圓上兩點(diǎn)，滿足SKIPIF1<0，且SKIPIF1<0，則橢圓C的離心率為________．10．（2023秋·河北邯鄲·高三統(tǒng)考期末）已知拋物線SKIPIF1<0的焦點(diǎn)為F，若SKIPIF1<0在拋物線C上，且滿足SKIPIF1<0，則SKIPIF1<0的最小值為______.四、解答題11．（2023·高三課時(shí)練習(xí)）已知SKIPIF1<0、SKIPIF1<0是雙曲線SKIPIF1<0的左、右焦點(diǎn).(1)求證：雙曲線C上任意一點(diǎn)M到雙曲線兩條漸近線的距離之積為常數(shù)