新高考數(shù)學(xué)二輪復(fù)習(xí) 小題綜合練專題10 解析幾何（原卷版）

專題10解析幾何小題綜合一、單選題1．（2023·浙江溫州·統(tǒng)考三模）已知直線SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．22．（2023·浙江金華·統(tǒng)考模擬預(yù)測(cè)）雙曲線SKIPIF1<0的漸近線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，若點(diǎn)SKIPIF1<0在拋物線上，且SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．4 D．84．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）已知圓SKIPIF1<0，圓心為SKIPIF1<0的圓分別與圓SKIPIF1<0相切.圓SKIPIF1<0的公切線（傾斜角為鈍角）交圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，則線段SKIPIF1<0的長度為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．65．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線與拋物線交于SKIPIF1<0兩點(diǎn)且SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·浙江溫州·樂清市知臨中學(xué)校考模擬預(yù)測(cè)）設(shè)過原點(diǎn)且傾斜角為SKIPIF1<0的直線與雙曲線C：SKIPIF1<0SKIPIF1<0的左，右支分別交于A、B兩點(diǎn)，F(xiàn)是C的焦點(diǎn)，若三角形SKIPIF1<0的面積大于SKIPIF1<0，則C的離心率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·浙江·校聯(lián)考二模）已知直線SKIPIF1<0和直線SKIPIF1<0，拋物線SKIPIF1<0上一動(dòng)點(diǎn)SKIPIF1<0到直線SKIPIF1<0直線SKIPIF1<0的距離之和的最小值是（

）A．2 B．3 C．SKIPIF1<0 D．SKIPIF1<08．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0右支上一點(diǎn)，SKIPIF1<0分別是SKIPIF1<0的左、右焦點(diǎn)，若SKIPIF1<0的角平分線與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的離心率為（

）A．2 B．SKIPIF1<0 C．3 D．SKIPIF1<09．（2023·浙江溫州·樂清市知臨中學(xué)?？级＃┮阎獧E圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過右焦點(diǎn)作傾斜角為SKIPIF1<0的直線交橢圓于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則橢圓的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·浙江金華·統(tǒng)考模擬預(yù)測(cè)）已知橢圓SKIPIF1<0為橢圓的右焦點(diǎn)，曲線SKIPIF1<0交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且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、多選題11．（2023·浙江·高三專題練習(xí)）若直線SKIPIF1<0與圓C：SKIPIF1<0相交于A，B兩點(diǎn)，則SKIPIF1<0的長度可能等于（

）A．2 B．3 C．4 D．512．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0是直線SKIPIF1<0上一點(diǎn)，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0，則（

）A．直線SKIPIF1<0經(jīng)過定點(diǎn)B．SKIPIF1<0的最小值為SKIPIF1<0C．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離的最大值為SKIPIF1<0D．SKIPIF1<0是銳角13．（2023·浙江金華·統(tǒng)考模擬預(yù)測(cè)）已知拋物線SKIPIF1<0，點(diǎn)SKIPIF1<0均在拋物線SKIPIF1<0上，點(diǎn)SKIPIF1<0，則（

）A．直線SKIPIF1<0的斜率可能為SKIPIF1<0B．線段SKIPIF1<0長度的最小值為SKIPIF1<0C．若SKIPIF1<0三點(diǎn)共線，則存在唯一的點(diǎn)SKIPIF1<0，使得點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)D．若SKIPIF1<0三點(diǎn)共線，則存在兩個(gè)不同的點(diǎn)SKIPIF1<0，使得點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)14．（2023·浙江溫州·樂清市知臨中學(xué)?？寄M預(yù)測(cè)）已知橢圓為SKIPIF1<0，設(shè)一個(gè)點(diǎn)始終在此橢圓內(nèi)運(yùn)動(dòng)，這個(gè)點(diǎn)從一個(gè)焦點(diǎn)出發(fā)沿直線，經(jīng)橢圓壁反彈后沿直線經(jīng)過另一個(gè)焦點(diǎn)，再經(jīng)橢圓壁反彈后沿直線回到這個(gè)焦點(diǎn)，稱這個(gè)過程為一次“活動(dòng)”，記此點(diǎn)進(jìn)行n次“活動(dòng)”的總路程為SKIPIF1<0，SKIPIF1<0，則不可能的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）已知SKIPIF1<0、SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，過點(diǎn)SKIPIF1<0作雙曲線的切線交雙曲線于點(diǎn)SKIPIF1<0（SKIPIF1<0在第一象限），點(diǎn)SKIPIF1<0在SKIPIF1<0延長線上，則下列說法正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0為SKIPIF1<0的平分線 D．SKIPIF1<0的角平分線所在直線的傾斜角為SKIPIF1<016．（2023·浙江紹興·統(tǒng)考二模）已知點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0的左右焦點(diǎn)，點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0上一點(diǎn)，點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0平分線的對(duì)稱點(diǎn)SKIPIF1<0也在橢圓SKIPIF1<0上，若SKIPIF1<0，則（

）A．SKIPIF1<0的周長為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0平分線的斜率為SKIPIF1<0 D．橢圓SKIPIF1<0的離心率為SKIPIF1<017．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）如圖，已知拋物線SKIPIF1<0，過拋物線焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0自上而下，分別交拋物線與圓SKIPIF1<0于SKIPIF1<0四點(diǎn)，則（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<018．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）雙曲線SKIPIF1<0的左、右焦點(diǎn)分別SKIPIF1<0，具有公共焦點(diǎn)的橢圓與雙曲線在第一象限的交點(diǎn)為SKIPIF1<0，雙曲線和橢圓的離心率分別為SKIPIF1<0的內(nèi)切圓的圓心為SKIPIF1<0，過SKIPIF1<0作直線SKIPIF1<0的垂線，垂足為SKIPIF1<0，則（

）A．SKIPIF1<0到SKIPIF1<0軸的距離為SKIPIF1<0B．點(diǎn)SKIPIF1<0的軌跡是雙曲線C．若SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<019．（2023·浙江嘉興·?？寄M預(yù)測(cè)）已知拋物線SKIPIF1<0：SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0均在拋物線SKIPIF1<0上，點(diǎn)SKIPIF1<0，則（

）A．直線SKIPIF1<0的斜率可能為SKIPIF1<0B．線段SKIPIF1<0長度的最小值為SKIPIF1<0C．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三點(diǎn)共線，則SKIPIF1<0是定值D．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三點(diǎn)共線，則存在兩組點(diǎn)對(duì)SKIPIF1<0，使得點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)20．（2023·浙江·校聯(lián)考二模）設(shè)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，圓SKIPIF1<0方程為SKIPIF1<0，直線SKIPIF1<0方程為SKIPIF1<0.則（

）A．對(duì)任意實(shí)數(shù)SKIPIF1<0和點(diǎn)SKIPIF1<0，直線SKIPIF1<0和圓SKIPIF1<0有公共點(diǎn)B．對(duì)任意點(diǎn)SKIPIF1<0，必存在實(shí)數(shù)SKIPIF1<0，使得直線SKIPIF1<0與圓SKIPIF1<0相切C．對(duì)任意實(shí)數(shù)SKIPIF1<0，必存在點(diǎn)SKIPIF1<0，使得直線SKIPIF1<0與圓SKIPIF1<0相切D．對(duì)任意實(shí)數(shù)SKIPIF1<0和點(diǎn)SKIPIF1<0，圓SKIPIF1<0和圓SKIPIF1<0上到直線SKIPIF1<0距離為1的點(diǎn)的個(gè)數(shù)相等21．（2023春·浙江杭州·高三浙江省杭州第二中學(xué)校聯(lián)考階段練習(xí)）已知SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0的垂線，垂足為SKIPIF1<0，則（

）A．直線SKIPIF1<0過定點(diǎn) B．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的最大距離為SKIPIF1<0C．SKIPIF1<0的最大值為3 D．SKIPIF1<0的最小值為222．（2023·浙江金華·統(tǒng)考模擬預(yù)測(cè)）如圖，已知SKIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0分別作兩條斜率互為相反數(shù)的直線SKIPIF1<0，交拋物線于SKIPIF1<0四點(diǎn)，且線段SKIPIF1<0相交于點(diǎn)SKIPIF1<0，則下列選項(xiàng)中正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<023．（2023·浙江·校聯(lián)考三模）已知橢圓SKIPIF1<0，其右焦點(diǎn)為SKIPIF1<0，以SKIPIF1<0為端點(diǎn)作SKIPIF1<0條射線交橢圓于SKIPIF1<0，且每兩條相鄰射線的夾角相等，則（

）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的面積的最小值為SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，過SKIPIF1<0作橢圓的切線SKIPIF1<0，且SKIPIF1<0交于點(diǎn)SKIPIF1<0交于點(diǎn)SKIPIF1<0，則SKIPIF1<0的斜率乘積為定值SKIPIF1<024．（2023·浙江溫州·樂清市知臨中學(xué)?？级＃┮阎獟佄锞€SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0（SKIPIF1<0為銳角）的直線交拋物線于SKIPIF1<0兩點(diǎn)（其中點(diǎn)A在第一象限）.如圖，把平面SKIPIF1<0沿SKIPIF1<0軸折起，使平面SKIPIF1<0平面SKIPIF1<0，則以下選項(xiàng)正確的為（

）

A．折疊前SKIPIF1<0的面積的最大值為SKIPIF1<0B．折疊前SKIPIF1<0平分SKIPIF1<0C．折疊后三棱錐SKIPIF1<0體積為定值SKIPIF1<0D．折疊后異面直線SKIPIF1<0所成角隨SKIPIF1<0的增大而增大三、填空題25．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0和圓SKIPIF1<0，則過點(diǎn)SKIPIF1<0且與SKIPIF1<0都相切的直線方程為__________.（寫出一條即可）26．（2023·浙江·高三專題練習(xí)）已知圓SKIPIF1<0，若SKIPIF1<0被兩坐標(biāo)軸截得的弦長相等，則SKIPIF1<0__________.27．（2023·浙江溫州·樂清市知臨中學(xué)?？寄M預(yù)測(cè)）點(diǎn)P圓SKIPIF1<0上，點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，O坐標(biāo)原點(diǎn)，且SKIPIF1<0，則點(diǎn)SKIPIF1<0的橫坐標(biāo)的取值范圍為___________．28．（2023·浙江紹興·紹興一中?？寄M預(yù)測(cè)）從點(diǎn)SKIPIF1<0射出兩條光線的方程分別為：SKIPIF1<0和SKIPIF1<0，經(jīng)SKIPIF1<0軸反射后都與圓SKIPIF1<0相切，則SKIPIF1<0__________．29．（2023·浙江紹興·統(tǒng)考模擬預(yù)測(cè)）已知圓SKIPIF1<0在橢圓SKIPIF1<0的內(nèi)部，SKIPIF1<0為SKIPIF1<0上的一個(gè)動(dòng)點(diǎn)，過SKIPIF1<0作SKIPIF1<0的一條切線，交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，切點(diǎn)為SKIPIF1<0，若當(dāng)SKIPIF1<0為SKIPIF1<0的中點(diǎn)時(shí)，直線SKIPIF1<0的傾斜角恰好為SKIPIF1<0，則該橢圓SKIPIF1<0的離心率SKIPIF1<0___________.30．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知橢圓SKIPIF1<0的上下頂點(diǎn)分別為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交橢圓于SKIPIF1<0兩點(diǎn)，記SKIPIF1<0，則SKIPIF1<0___________.31．（2023春·浙江杭州·高三浙江省杭州第二中學(xué)校聯(lián)考階段練習(xí)）考慮這樣的等腰三角形：它的三個(gè)頂點(diǎn)都在橢圓SKIPIF1<0：SKIPIF1<0上，且其中恰有兩個(gè)頂點(diǎn)為橢圓SKIPIF1<0的頂點(diǎn)．這樣的等腰三角形有________個(gè).32．（2023·浙江寧波·鎮(zhèn)海中學(xué)校考模擬預(yù)測(cè)）已知橢圓SKIPIF1<0，SKIPIF1<0、SKIPIF1<0分別是其左，右焦點(diǎn)，P為橢圓C上非長軸端點(diǎn)的任意一點(diǎn)，D是x軸上一點(diǎn)，使得SKIPIF1<0平分SKIPIF1<0．過點(diǎn)D作SKIPIF1<0、SKIPIF1<0的垂線，垂足分別為A、B．則SKIPIF1<0的最大值是__________．33．（2023·浙江·校聯(lián)考三模）已知拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0點(diǎn)的橫坐標(biāo)為___________.34．（2023·浙江杭州·統(tǒng)考一模）已知點(diǎn)SKIPIF1<0，直線SKIPIF1<0與圓：SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為等腰直角三角形，則直線SKIPIF1<0的方程為______SKIPIF1<0寫出一條即可SKIPIF1<035．（2023·浙江·高三專題練習(xí)）已知圓SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0兩