答案第=page11頁(yè)，共=sectionpages22頁(yè)專(zhuān)題19直線和圓【練基礎(chǔ)】單選題1．（2023·浙江嘉興·統(tǒng)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，SKIPIF1<0與直線SKIPIF1<0，若在直線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·山西·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0：SKIPIF1<0的圓心到直線SKIPIF1<0的距離為SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0的公切線共有（

）A．0條 B．1條 C．2條 D．3條3．（2023·黑龍江哈爾濱·哈爾濱三中校考一模）已知SKIPIF1<0，SKIPIF1<0，若直線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023·河南·長(zhǎng)葛市第一高級(jí)中學(xué)統(tǒng)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0是雙曲線SKIPIF1<0的右焦點(diǎn)，點(diǎn)SKIPIF1<0是雙曲線上位于第一象限內(nèi)的一點(diǎn)，且SKIPIF1<0與SKIPIF1<0軸垂直，點(diǎn)SKIPIF1<0是雙曲線漸近線上的動(dòng)點(diǎn)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·內(nèi)蒙古·校聯(lián)考模擬預(yù)測(cè)）已知直線SKIPIF1<0被圓SKIPIF1<0截得的線段長(zhǎng)為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·山東泰安·統(tǒng)考一模）已知直線SKIPIF1<0與圓SKIPIF1<0相切，與拋物線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，以SKIPIF1<0為直徑的圓過(guò)坐標(biāo)原點(diǎn)，則直線SKIPIF1<0的方程為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<07．（2023·河南開(kāi)封·開(kāi)封高中校考模擬預(yù)測(cè)）已知曲線SKIPIF1<0的方程為SKIPIF1<0，曲線SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對(duì)稱曲線為SKIPIF1<0，若以曲線SKIPIF1<0與兩坐標(biāo)軸的交點(diǎn)為頂點(diǎn)的四邊形面積為SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．1 C．0或SKIPIF1<0 D．08．（2023·陜西西安·統(tǒng)考一模）已知雙曲線C：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)SKIPIF1<0的直線與圓SKIPIF1<0相切于點(diǎn)Q，與雙曲線的右支交于點(diǎn)P，若線段SKIPIF1<0的垂直平分線恰好過(guò)右焦點(diǎn)SKIPIF1<0，則雙曲線C的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．2二、多選題9．（2023·山東菏澤·統(tǒng)考一模）已知圓SKIPIF1<0，下列說(shuō)法正確有（

）A．對(duì)于SKIPIF1<0，直線SKIPIF1<0與圓SKIPIF1<0都有兩個(gè)公共點(diǎn)B．圓SKIPIF1<0與動(dòng)圓SKIPIF1<0有四條公切線的充要條件是SKIPIF1<0C．過(guò)直線SKIPIF1<0上任意一點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線SKIPIF1<0（SKIPIF1<0為切點(diǎn)），則四邊形SKIPIF1<0的面積的最小值為4D．圓SKIPIF1<0上存在三點(diǎn)到直線SKIPIF1<0距離均為110．（2023·廣東佛山·統(tǒng)考一模）設(shè)單位圓O與x軸的左、右交點(diǎn)分別為A、B，直線l：SKIPIF1<0（其中SKIPIF1<0）分別與直線SKIPIF1<0、SKIPIF1<0交于C、D兩點(diǎn)，則（

）A．SKIPIF1<0時(shí)，l的傾斜角為SKIPIF1<0B．SKIPIF1<0，點(diǎn)A、B到l的距離之和為定值C．SKIPIF1<0，使l與圓O無(wú)公共點(diǎn)D．SKIPIF1<0，恒有SKIPIF1<011．（2023·全國(guó)·模擬預(yù)測(cè)）設(shè)直線l：SKIPIF1<0，圓C：SKIPIF1<0，若直線l與圓C恒有兩個(gè)公共點(diǎn)A，B，則下列說(shuō)法正確的是（

）A．r的取值范圍是SKIPIF1<0B．若r的值固定不變，則當(dāng)SKIPIF1<0時(shí)∠ACB最小C．若r的值固定不變，則SKIPIF1<0的面積的最大值為SKIPIF1<0D．若SKIPIF1<0，則當(dāng)SKIPIF1<0的面積最大時(shí)直線l的斜率為1或SKIPIF1<012．（2023·遼寧沈陽(yáng)·統(tǒng)考一模）已知圓SKIPIF1<0，點(diǎn)SKIPIF1<0是直線SKIPIF1<0上的動(dòng)點(diǎn)，過(guò)點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，則下列說(shuō)法正確的是（

）A．切線長(zhǎng)SKIPIF1<0的最小值為SKIPIF1<0B．四邊形SKIPIF1<0面積的最小值為SKIPIF1<0C．若SKIPIF1<0是圓SKIPIF1<0的一條直徑，則SKIPIF1<0的最小值為SKIPIF1<0D．直線SKIPIF1<0恒過(guò)定點(diǎn)SKIPIF1<0三、填空題13．（2023·寧夏銀川·六盤(pán)山高級(jí)中學(xué)校考一模）圓心在直線SKIPIF1<0上，且過(guò)點(diǎn)SKIPIF1<0的圓的標(biāo)準(zhǔn)方程為_(kāi)_________．14．（2023·江西贛州·統(tǒng)考一模）已知函數(shù)SKIPIF1<0且SKIPIF1<0的圖像恒過(guò)定點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0在圓SKIPIF1<0外，則符合條件的整數(shù)SKIPIF1<0的取值可以為_(kāi)_________.（寫(xiě)出一個(gè)值即可）15．（2023·黑龍江·黑龍江實(shí)驗(yàn)中學(xué)校考一模）古希臘數(shù)學(xué)家阿波羅尼斯發(fā)現(xiàn)如下結(jié)論：“平面內(nèi)到兩個(gè)定點(diǎn)A，B的距離之比為定值SKIPIF1<0的點(diǎn)的軌跡是圓”．在平面直角坐標(biāo)系中，已知點(diǎn)SKIPIF1<0，點(diǎn)P滿足SKIPIF1<0，設(shè)點(diǎn)P的軌跡為圓M，點(diǎn)M為圓心，若直線SKIPIF1<0與圓M相交于D，G兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0____________．16．（2023·河南·校聯(lián)考模擬預(yù)測(cè)）圓SKIPIF1<0與x軸交于A，B兩點(diǎn)(A在B的左側(cè))，點(diǎn)N滿足SKIPIF1<0，直線SKIPIF1<0與圓M和點(diǎn)N的軌跡同時(shí)相切，則直線l的斜率為_(kāi)_______．四、解答題17．（2022·云南昆明·昆明一中模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，動(dòng)點(diǎn)M滿足SKIPIF1<0，點(diǎn)M的軌跡為曲線C．(1)求曲線C的軌跡方程；(2)曲線C上任意一點(diǎn)N（不同于A，B）和點(diǎn)A，B的連線分別與y軸交于P，Q兩點(diǎn)，O為坐標(biāo)原點(diǎn)求證：SKIPIF1<0為定值．18．（2022·河南鶴壁·鶴壁高中校考模擬預(yù)測(cè)）已知圓SKIPIF1<0：SKIPIF1<0，點(diǎn)SKIPIF1<0是直線SKIPIF1<0：SKIPIF1<0上一動(dòng)點(diǎn)，過(guò)點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線SKIPIF1<0，SKIPIF1<0，切點(diǎn)分別是SKIPIF1<0和SKIPIF1<0．(1)試問(wèn)直線SKIPIF1<0是否恒過(guò)定點(diǎn)，若是求出這個(gè)定點(diǎn)，若否說(shuō)明理由；(2)直線SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求SKIPIF1<0的取值范圍（SKIPIF1<0為坐標(biāo)原點(diǎn)）．【提能力】一、單選題19．（2023·甘肅蘭州·蘭州五十九中校考模擬預(yù)測(cè)）在平面直角坐標(biāo)系xOy中，已知圓C：x2＋y2－4x＝0及點(diǎn)A(－1,0)，B(1,2)，在圓C上存在點(diǎn)P，使得|PA|2＋|PB|2＝12，則點(diǎn)P的個(gè)數(shù)為（

）A．1 B．2 C．3 D．420．（2023·山東濰坊·校考一模）已知平面向量SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．（2023·浙江·永嘉中學(xué)校聯(lián)考模擬預(yù)測(cè)）已知直角SKIPIF1<0的直角頂點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，若點(diǎn)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．（2023·全國(guó)·校聯(lián)考模擬預(yù)測(cè)）阿波羅尼斯是古希臘著名數(shù)學(xué)家，與歐幾里得?阿基米德被稱為亞歷山大時(shí)期數(shù)學(xué)三巨匠，阿波羅尼斯發(fā)現(xiàn)：平面內(nèi)到兩個(gè)定點(diǎn)SKIPIF1<0的距離之比為定值SKIPIF1<0，且SKIPIF1<0的點(diǎn)的軌跡是圓，此圓被稱為“阿波羅尼斯圓”.在平面直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0.設(shè)點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0，則下列說(shuō)法錯(cuò)誤的是（

）A．SKIPIF1<0的方程為SKIPIF1<0B．當(dāng)SKIPIF1<0三點(diǎn)不共線時(shí)，則SKIPIF1<0C．在C上存在點(diǎn)M，使得SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<023．（2023·全國(guó)·模擬預(yù)測(cè)）已知點(diǎn)P是圓SKIPIF1<0上一點(diǎn)，若點(diǎn)P到直線SKIPIF1<0的距離為1，則滿足條件的點(diǎn)P的個(gè)數(shù)為（

）A．1 B．2 C．3 D．424．（2023·四川涼山·統(tǒng)考一模）已知SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，過(guò)SKIPIF1<0作垂直SKIPIF1<0軸的直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，以SKIPIF1<0為直徑的圓交SKIPIF1<0軸于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023·湖南長(zhǎng)沙·統(tǒng)考一模）在平面直角坐標(biāo)系SKIPIF1<0中,已知SKIPIF1<0,SKIPIF1<0SKIPIF1<0,若該平面中存在點(diǎn)SKIPIF1<0,同時(shí)滿足兩個(gè)條件SKIPIF1<0與SKIPIF1<0,則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<026．（2022·北京·統(tǒng)考模擬預(yù)測(cè)）在平面直角坐標(biāo)系中，已知點(diǎn)P在直線SKIPIF1<0上，且點(diǎn)P在第四象限，點(diǎn)SKIPIF1<0．以PQ為直徑的圓C與直線l的另外一個(gè)交點(diǎn)為T(mén)，滿足SKIPIF1<0，則圓C的直徑為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題27．（2023·安徽馬鞍山·統(tǒng)考一模）已知直線SKIPIF1<0與圓SKIPIF1<0，則（

）A．直線SKIPIF1<0必過(guò)定點(diǎn) B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0被圓SKIPIF1<0截得的弦長(zhǎng)為SKIPIF1<0C．直線SKIPIF1<0與圓SKIPIF1<0可能相切 D．直線SKIPIF1<0與圓SKIPIF1<0不可能相離28．（2023·遼寧·遼寧實(shí)驗(yàn)中學(xué)校考模擬預(yù)測(cè)）已知圓SKIPIF1<0，圓SKIPIF1<0，則（

）A．無(wú)論k取何值，圓心SKIPIF1<0始終在直線SKIPIF1<0上B．若圓O與圓SKIPIF1<0有公共點(diǎn)，則實(shí)數(shù)k的取值范圍為SKIPIF1<0C．若圓O與圓SKIPIF1<0的公共弦長(zhǎng)為SKIPIF1<0，則SKIPIF1<0或SKIPIF1<0D．與兩個(gè)圓都相切的直線叫做這兩個(gè)圓的公切線，如果兩個(gè)圓在公切線的同側(cè)，則這條公切線叫做這兩個(gè)圓的外公切線，當(dāng)SKIPIF1<0時(shí)，兩圓的外公切線長(zhǎng)為SKIPIF1<029．（2023·山東濰坊·校考一模）已知SKIPIF1<0是圓SKIPIF1<0上的兩點(diǎn)，則下列結(jié)論中正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．若點(diǎn)O到直線SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0的最大值為4D．SKIPIF1<0的最小值為SKIPIF1<030．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0，圓SKIPIF1<0，下列說(shuō)法正確的是（

）A．若SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0相交B．若SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0外離C．若直線SKIPIF1<0與圓SKIPIF1<0相交，則SKIPIF1<0D．若直線SKIPIF1<0與圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0三、填空題31．（2023·江西南昌·統(tǒng)考一模）已知一簇圓SKIPIF1<0，直線l：y＝kx＋b是它們的一條公切線，則k＋b＝______．32．（2023·吉林·東北師大附中校考二模）在平面直角坐標(biāo)系SKIPIF1<0中，已知?jiǎng)訄ASKIPIF1<0的方程為SKIPIF1<0，則圓心SKIPIF1<0的軌跡方程為_(kāi)___________．若對(duì)于圓SKIPIF1<0上的任意點(diǎn)SKIPIF1<0，在圓SKIPIF1<0：SKIPIF1<0上均存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則滿足條件的圓心SKIPIF1<0的軌跡長(zhǎng)度為_(kāi)_____．33．（2023·安徽·統(tǒng)考一模）已知圓SKIPIF1<0，直線SKIPIF1<0（SKIPIF1<0是參數(shù)），則直線SKIPIF1<0被圓SKIPIF1<0截得的弦長(zhǎng)的最小值為_(kāi)_________.34．（2023·湖南·模擬預(yù)測(cè)）在平面直角坐標(biāo)系SKIPIF1<0中，已知圓SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0與圓SKIPIF1<0相切，與圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，分別以點(diǎn)SKIPIF1<0，SKIPIF1<0為切點(diǎn)作圓SKIPIF1<0的切線SKIPIF1<0，SKIPIF1<0設(shè)直線SKIPIF1<0，SKIPIF1<0的交點(diǎn)為SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)_________．四、解答題35．（2021·山東棗莊·統(tǒng)考二模）已知?jiǎng)狱c(diǎn)M與兩個(gè)定點(diǎn)O(0，0)，A(3，0)的距離的比為SKIPIF1<0，動(dòng)點(diǎn)M的軌跡為曲線C．(1)求C的軌跡方程，并說(shuō)明其形狀；(2)過(guò)直線x＝3上的動(dòng)點(diǎn)P(3，p)(p≠0)分別作C的兩條切線PQ、PR(Q、R為切點(diǎn))，N為弦QR的中點(diǎn)，直線l：3x＋4y＝6分別與x軸、y軸交于點(diǎn)E、F，求△NEF的面積S的取值范圍．36．（2022·廣西·統(tǒng)考模擬預(yù)測(cè)）已知拋物線SKIPIF1<0