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34 圓錐曲線中的綜合問題(原卷版)

專題34圓錐曲線中的綜合問題一、單選題1．已知右焦點(diǎn)為SKIPIF1<0的橢圓SKIPIF1<0：SKIPIF1<0上的三點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0滿足直線SKIPIF1<0過坐標(biāo)原點(diǎn)，若SKIPIF1<0于點(diǎn)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的離心率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的準(zhǔn)線的垂線，垂足為SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．1 B．SKIPIF1<0 C．2 D．SKIPIF1<03．已知拋物線SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線上，斜率為1的直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)．直線SKIPIF1<0、SKIPIF1<0的斜率分別記為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．1 B．2 C．3 D．44．設(shè)橢圓SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，過SKIPIF1<0且斜率為SKIPIF1<0的直線交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn)（SKIPIF1<0在SKIPIF1<0軸上方）.SKIPIF1<0關(guān)于SKIPIF1<0軸的對(duì)稱點(diǎn)為SKIPIF1<0，連接SKIPIF1<0并延長交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等比數(shù)列，則橢圓的離心率SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知橢圓SKIPIF1<0，斜率為SKIPIF1<0的直線與橢圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0在SKIPIF1<0軸左側(cè)，且SKIPIF1<0點(diǎn)在SKIPIF1<0軸上方，點(diǎn)SKIPIF1<0關(guān)于坐標(biāo)原點(diǎn)SKIPIF1<0對(duì)稱的點(diǎn)為SKIPIF1<0，且SKIPIF1<0，則該橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知橢圓SKIPIF1<0與雙曲線SKIPIF1<0具有相同的左、右焦點(diǎn)SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為它們?cè)诘谝幌笙薜慕稽c(diǎn)，動(dòng)點(diǎn)SKIPIF1<0在曲線SKIPIF1<0上，若記曲線SKIPIF1<0，SKIPIF1<0的離心率分別為SKIPIF1<0，SKIPIF1<0，滿足SKIPIF1<0，且直線SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)的坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知過點(diǎn)SKIPIF1<0的直線與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0一定是（

）A．等腰三角形 B．直角三角形C．有一個(gè)角為SKIPIF1<0的三角形 D．面積為定值的三角形8．如圖所示，SKIPIF1<0，SKIPIF1<0是雙曲線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）的左、右焦點(diǎn)，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左支的交點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則雙曲線SKIPIF1<0的漸近線方程為（

）

A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．已知拋物線SKIPIF1<0的焦點(diǎn)為F，SKIPIF1<0，SKIPIF1<0是C上相異兩點(diǎn)，則下列結(jié)論正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0 B．若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<010．設(shè)SKIPIF1<0為雙曲線SKIPIF1<0：SKIPIF1<0上一動(dòng)點(diǎn)，SKIPIF1<0，SKIPIF1<0為上、下焦點(diǎn)，SKIPIF1<0為原點(diǎn)，則下列結(jié)論正確的是（

）A．若點(diǎn)SKIPIF1<0，則SKIPIF1<0最小值為7B．若過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)（SKIPIF1<0與SKIPIF1<0均不重合），則SKIPIF1<0C．若點(diǎn)SKIPIF1<0，SKIPIF1<0在雙曲線SKIPIF1<0的上支，則SKIPIF1<0最小值為SKIPIF1<0D．過SKIPIF1<0的直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0不同兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0有4條11．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0為拋物線上兩個(gè)位于第一象限的動(dòng)點(diǎn)，且有SKIPIF1<0．直線SKIPIF1<0與準(zhǔn)線分別交于SKIPIF1<0兩點(diǎn)，則下列說法正確的是（

）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 D．當(dāng)SKIPIF1<0時(shí)，延長SKIPIF1<0交準(zhǔn)線于SKIPIF1<012．已知橢圓SKIPIF1<0的左，右兩焦點(diǎn)分別是SKIPIF1<0，其中SKIPIF1<0.直線SKIPIF1<0與橢圓交于SKIPIF1<0兩點(diǎn)，則下列說法中正確的有（

）A．SKIPIF1<0的周長為SKIPIF1<0B．若SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則橢圓的離心率的取值范圍是SKIPIF1<0D．若SKIPIF1<0時(shí)，則SKIPIF1<0的面積是SKIPIF1<0三、填空題13．已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，P是C右支上一點(diǎn)，線段SKIPIF1<0與C的左支交于點(diǎn)M．若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的離心率為．14．已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，過直線SKIPIF1<0上一點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0．則SKIPIF1<0的取值范圍為．15．已知雙曲線SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，離心率為e，直線SKIPIF1<0分別與C的左、右兩支交于點(diǎn)M，N.若SKIPIF1<0的面積為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為16．已知點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，圓SKIPIF1<0與直線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，與線段SKIPIF1<0相交于點(diǎn)SKIPIF1<0，且SKIPIF1<0．若SKIPIF1<0是線段SKIPIF1<0上靠近SKIPIF1<0的四等分點(diǎn)，則拋物線SKIPIF1<0的方程為．四、解答題17．已知橢圓SKIPIF1<0的左、右焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，離心率為SKIPIF1<0．點(diǎn)P是橢圓C上不同于頂點(diǎn)的任意一點(diǎn)，射線SKIPIF1<0、SKIPIF1<0分別與橢圓C交于點(diǎn)A、B，SKIPIF1<0的周長為8．(1)求橢圓C的標(biāo)準(zhǔn)方程；(2)若SKIPIF1<0，SKIPIF1<0，求證：SKIPIF1<0為定值．18．在平面直角坐標(biāo)系中，已知點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在直線SKIPIF1<0上運(yùn)動(dòng)，過點(diǎn)SKIPIF1<0與SKIPIF1<0垂直的直線和SKIPIF1<0的中垂線相交于點(diǎn)SKIPIF1<0.(1)求動(dòng)點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；(2)設(shè)點(diǎn)SKIPIF1<0是軌跡SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0軸上，圓SKIPIF1<0內(nèi)切于SKIPIF1<0，求SKIPIF1<0的面積的最小值.19．已知橢圓SKIPIF1<0：SKIPIF1<0．(1)直線SKIPIF1<0：SKIPIF1<0交橢圓SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求線段SKIPIF1<0的長；(2)SKIPIF1<0為橢圓SKIPIF1<0的左頂點(diǎn)，記直線SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，試問直線SKIPIF1<0是否過定點(diǎn)，若是，求出定點(diǎn)坐標(biāo)，若不是，請(qǐng)說明理由．20．已知雙曲線SKIPIF1<0的離心率為2，右焦點(diǎn)SKIPIF1<0到一條漸近線的距離為SKIPIF1<0.(1)求雙曲線SKIPIF1<0的方程；(2)已知點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0與雙曲線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，求直線SKIPIF1<0的方程.21．已知雙曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，漸近線方程為SKIPIF1<0.(1)求雙曲線SKIPIF1<0的方程；(2)過SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，過SKIPIF1<