新高考數(shù)學(xué)二輪復(fù)習(xí)核心考點(diǎn)講與練重難點(diǎn)11九種直線和圓的方程的解題方法原卷版

重難點(diǎn)11九種直線和圓的方程的解題方法（核心考點(diǎn)講與練）題型一：直接法求直線方程一、單選題1．（2022·全國·高三專題練習(xí)）直線l經(jīng)過兩條直線SKIPIF1<0和SKIPIF1<0的交點(diǎn)，且平行于直線SKIPIF1<0，則直線l的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)（文））若經(jīng)過點(diǎn)SKIPIF1<0的直線與圓SKIPIF1<0相切，則該直線在y軸上的截距為(

)A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江·高三專題練習(xí)）如圖，圓SKIPIF1<0、SKIPIF1<0在第一象限，且與SKIPIF1<0軸，直線SKIPIF1<0均相切，則圓心SKIPIF1<0、SKIPIF1<0所在直線的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·重慶·高三開學(xué)考試）若直線SKIPIF1<0交圓SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，且弦SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則SKIPIF1<0方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．（2022·全國·高三專題練習(xí)）過點(diǎn)SKIPIF1<0且在兩坐標(biāo)軸上截距相等的直線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．直線SKIPIF1<0與線段SKIPIF1<0有公共點(diǎn)B．直線SKIPIF1<0的傾斜角大于SKIPIF1<0C．SKIPIF1<0的邊SKIPIF1<0上的中線所在直線的方程為SKIPIF1<0D．SKIPIF1<0的邊SKIPIF1<0上的高所在直線的方程為SKIPIF1<07．（2022·全國·高三專題練習(xí)）已知直線l過點(diǎn)P（－1，1），且與直線SKIPIF1<0以及x軸圍成一個(gè)底邊在x軸上的等腰三角形，則下列結(jié)論正確的是（

）A．直線l與直線l1的斜率互為相反數(shù) B．所圍成的等腰三角形面積為1C．直線l關(guān)于原點(diǎn)的對(duì)稱直線方程為SKIPIF1<0 D．原點(diǎn)到直線l的距離為SKIPIF1<08．（2021·全國·模擬預(yù)測(cè)）已知平面上的線段SKIPIF1<0及點(diǎn)SKIPIF1<0，任取SKIPIF1<0上一點(diǎn)SKIPIF1<0，稱線段SKIPIF1<0長度的最小值為點(diǎn)SKIPIF1<0到線段SKIPIF1<0的距離，記作SKIPIF1<0.已知線段SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為平面上一點(diǎn)，且滿足SKIPIF1<0，若點(diǎn)SKIPIF1<0的軌跡為曲線SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是第一象限內(nèi)曲線SKIPIF1<0上兩點(diǎn)，點(diǎn)SKIPIF1<0且SKIPIF1<0，SKIPIF1<0，則（

）A．曲線SKIPIF1<0關(guān)于SKIPIF1<0軸對(duì)稱 B．點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0C．點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0 D．SKIPIF1<0的面積為SKIPIF1<0題型二：待定系數(shù)法求直線方程一、單選題1．（2022·內(nèi)蒙古·滿洲里市教研培訓(xùn)中心模擬預(yù)測(cè)（理））已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，準(zhǔn)線與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在第一象限且在拋物線SKIPIF1<0上，則當(dāng)SKIPIF1<0取得最大值時(shí)，直線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0=SKIPIF1<0+2 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）若直線SKIPIF1<0與SKIPIF1<0互相平行，且SKIPIF1<0過點(diǎn)SKIPIF1<0，則直線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)）已知直線SKIPIF1<0在SKIPIF1<0軸與SKIPIF1<0軸上的截距相等，則實(shí)數(shù)SKIPIF1<0的值是（

）A．1 B．﹣1 C．﹣2或1 D．2或14．（2022·全國·高三專題練習(xí)）過點(diǎn)SKIPIF1<0作直線SKIPIF1<0，滿足在兩坐標(biāo)軸上截距的絕對(duì)值相等的直線SKIPIF1<0有（

）條.A．1 B．2 C．3 D．4二、多選題5．（2021·重慶梁平·高三階段練習(xí)）已知直線SKIPIF1<0：SKIPIF1<0，則下列結(jié)論正確的是（

）A．直線SKIPIF1<0的傾斜角是SKIPIF1<0B．若直線SKIPIF1<0：SKIPIF1<0，則SKIPIF1<0C．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離是SKIPIF1<0D．過SKIPIF1<0與直線SKIPIF1<0平行的直線方程是SKIPIF1<06．（2022·全國·高三專題練習(xí)）下列命題正確的是（

）A．已知點(diǎn)SKIPIF1<0，SKIPIF1<0，若直線SKIPIF1<0與線段SKIPIF1<0有交點(diǎn)，則SKIPIF1<0或SKIPIF1<0B．SKIPIF1<0是直線SKIPIF1<0：SKIPIF1<0與直線SKIPIF1<0：SKIPIF1<0垂直的充分不必要條件C．經(jīng)過點(diǎn)SKIPIF1<0且在SKIPIF1<0軸和SKIPIF1<0軸上的截距都相等的直線的方程為SKIPIF1<0D．已知直線SKIPIF1<0SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，SKIPIF1<0，和兩點(diǎn)SKIPIF1<0，SKIPIF1<0，如果SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0，則SKIPIF1<0的最大值是SKIPIF1<0.7．（2022·全國·高三專題練習(xí)）下列說法錯(cuò)誤的是（

）A．若直線SKIPIF1<0與直線SKIPIF1<0互相垂直，則SKIPIF1<0B．直線SKIPIF1<0的傾斜角的取值范圍是SKIPIF1<0C．SKIPIF1<0四點(diǎn)不在同一個(gè)圓上D．經(jīng)過點(diǎn)SKIPIF1<0且在x軸和y軸上截距都相等的直線方程為SKIPIF1<08．（2021·全國·高三專題練習(xí)）直線SKIPIF1<0與圓SKIPIF1<0相切，且SKIPIF1<0在SKIPIF1<0軸、SKIPIF1<0軸上的截距相等，則直線SKIPIF1<0的方程可能是A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題9．（2022·全國·高三專題練習(xí)（理））已知拋物線SKIPIF1<0的焦點(diǎn)為F，過焦點(diǎn)F的直線C交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則直線AB的方程為______．10．（2020·黑龍江·哈師大附中高三期末（理））若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0將圓SKIPIF1<0的周長分為SKIPIF1<0兩部分，則直線SKIPIF1<0的斜率為___________.四、解答題11．（2022·全國·高三專題練習(xí)）已知圓SKIPIF1<0：SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0.(1)過點(diǎn)SKIPIF1<0，作圓SKIPIF1<0的切線SKIPIF1<0，求切線SKIPIF1<0的方程；(2)判斷直線SKIPIF1<0與圓SKIPIF1<0是否相交，若相交，求出直線SKIPIF1<0被圓截得的弦長最短時(shí)m的值及最短弦長；若不相交，請(qǐng)說明理由.12．（2022·全國·高三專題練習(xí)）已知橢圓SKIPIF1<0的中心在原點(diǎn)，焦點(diǎn)在SKIPIF1<0軸上，左右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上.（1）求橢圓SKIPIF1<0的方程；（2）過SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0的面積為SKIPIF1<0，求以SKIPIF1<0為圓心且與直線SKIPIF1<0相切的圓的方程.題型三：已知兩直線位置關(guān)系求參數(shù)值或范圍一、單選題1．（2022·四川涼山·三模（理））已知直線SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·遼寧·二模）己知直線SKIPIF1<0，直線SKIPIF1<0，則SKIPIF1<0的充要條件是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題3．（2021·重慶一中高三階段練習(xí)）下列說法正確的有（

）A．若SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0：SKIPIF1<0與SKIPIF1<0：SKIPIF1<0平行”的充要條件B．當(dāng)圓SKIPIF1<0截直線SKIPIF1<0：SKIPIF1<0所得的弦長最短時(shí)，SKIPIF1<0C．若圓SKIPIF1<0：SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0有且僅有兩條公切線，則SKIPIF1<0D．直線SKIPIF1<0：SKIPIF1<0的傾斜角為139°4．（2021·廣東·高三階段練習(xí)）已知直線SKIPIF1<0過點(diǎn)SKIPIF1<0且與圓SKIPIF1<0：SKIPIF1<0相切，直線SKIPIF1<0與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0是圓SKIPIF1<0上的動(dòng)點(diǎn)，則下列結(jié)論中正確的有（

）A．點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0B．SKIPIF1<0面積的最大值為10C．當(dāng)直線SKIPIF1<0與直線SKIPIF1<0垂直時(shí)，SKIPIF1<0D．SKIPIF1<0的最大值為SKIPIF1<0三、填空題5．（2022·陜西·安康市高新中學(xué)三模（理））若雙曲線SKIPIF1<0的一條漸近線SKIPIF1<0與直線SKIPIF1<0平行，則直線SKIPIF1<0，SKIPIF1<0間的距離為______．6．（2022·天津·二模）在平面直角坐標(biāo)系SKIPIF1<0中，已知圓SKIPIF1<0，直線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，若對(duì)任意的實(shí)數(shù)SKIPIF1<0，直線SKIPIF1<0被圓SKIPIF1<0截得的弦長都是定值，則直線SKIPIF1<0的方程為___________.四、解答題7．（2022·全國·高三專題練習(xí)）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線SKIPIF1<0平行于直線SKIPIF1<0，且點(diǎn)SKIPIF1<0在第三象限．(1)求SKIPIF1<0的坐標(biāo)；(2)若直線SKIPIF1<0，且l也過切點(diǎn)SKIPIF1<0，求直線l的方程．8．（2020·江蘇·南京師大附中模擬預(yù)測(cè)）如圖，在平面直角坐標(biāo)系SKIPIF1<0中，已知圓SKIPIF1<0，圓SKIPIF1<0，A是第一象限內(nèi)的一點(diǎn)，其坐標(biāo)為SKIPIF1<0．

（1）若SKIPIF1<0，求t的值；（2）過A點(diǎn)作斜率為k的直線l，①若直線l和圓SKIPIF1<0，圓SKIPIF1<0均相切，求k的值；②若直線l和圓SKIPIF1<0，圓SKIPIF1<0分別相交于SKIPIF1<0和SKIPIF1<0，且SKIPIF1<0，求t的最小值．題型四：求解直線的定點(diǎn)一、單選題1．（2022·山東濱州·二模）已知直線SKIPIF1<0，圓SKIPIF1<0，則直線l與圓C的位置關(guān)系是（

）A．相離 B．相切 C．相交 D．不確定2．（2022·陜西·榆林市教育科學(xué)研究所模擬預(yù)測(cè)（理））在平面直角坐標(biāo)系SKIPIF1<0中，已知圓SKIPIF1<0，若曲線SKIPIF1<0上存在四個(gè)點(diǎn)SKIPIF1<0，過動(dòng)點(diǎn)Pi作圓O的兩條切線，A，B為切點(diǎn)，滿足SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題3．（2022·湖南·長沙市明德中學(xué)二模）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，SKIPIF1<0是圓SKIPIF1<0的兩條切線，SKIPIF1<0為切點(diǎn)，則（

）A．直線SKIPIF1<0恒過定點(diǎn)SKIPIF1<0B．當(dāng)SKIPIF1<0為正三角形時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的取值范圍為SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值為SKIPIF1<04．（2022·江蘇鹽城·三模）設(shè)直線l：SKIPIF1<0，交圓C：SKIPIF1<0于A，B兩點(diǎn)，則下列說法正確的有（

）A．直線l恒過定點(diǎn)SKIPIF1<0B．弦AB長的最小值為4C．當(dāng)SKIPIF1<0時(shí)，圓C關(guān)于直線l對(duì)稱的圓的方程為：SKIPIF1<0D．過坐標(biāo)原點(diǎn)O作直線l的垂線，垂足為點(diǎn)M，則線段MC長的最小值為SKIPIF1<05．（2022·重慶·高三階段練習(xí)）在平面直角坐標(biāo)系xOy中，圓SKIPIF1<0，若曲線SKIPIF1<0上存在四個(gè)點(diǎn)SKIPIF1<0，過動(dòng)點(diǎn)SKIPIF1<0作圓O的兩條切線，A，B為切點(diǎn)，滿足SKIPIF1<0，則k的值可能為（

）A．-7 B．-5 C．-2 D．–1三、雙空題6．（2022·北京房山·二模）已知圓SKIPIF1<0和直線SKIPIF1<0，則圓心坐標(biāo)為___________；若點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)，SKIPIF1<0到直線SKIPIF1<0的距離記為SKIPIF1<0，則SKIPIF1<0的最大值為___________.四、填空題7．（2022·河南焦作·三模（文））已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，其圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若方程SKIPIF1<0的所有根的和為6，則實(shí)數(shù)SKIPIF1<0的取值范圍是______．五、解答題8．（2022·全國·高三專題練習(xí)）SKIPIF1<0為坐標(biāo)原點(diǎn)，動(dòng)點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，過SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0.(1)求點(diǎn)SKIPIF1<0的軌跡方程；(2)設(shè)點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，且SKIPIF1<0，直線SKIPIF1<0過點(diǎn)SKIPIF1<0且垂直于SKIPIF1<0，求證：直線過定點(diǎn).9．（2022·全國·高三專題練習(xí)）在平面直角坐標(biāo)系SKIPIF1<0中，如圖，已知橢圓SKIPIF1<0的左、右頂點(diǎn)為SKIPIF1<0、SKIPIF1<0，右焦點(diǎn)為SKIPIF1<0，設(shè)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0、SKIPIF1<0與此橢圓分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0、SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0，SKIPIF1<0(1)設(shè)動(dòng)點(diǎn)SKIPIF1<0滿足SKIPIF1<0，求點(diǎn)SKIPIF1<0的軌跡方程；(2)設(shè)SKIPIF1<0，SKIPIF1<0，求點(diǎn)SKIPIF1<0的坐標(biāo)；(3)若點(diǎn)SKIPIF1<0在點(diǎn)SKIPIF1<0的軌跡上運(yùn)動(dòng)，問直線SKIPIF1<0是否經(jīng)過SKIPIF1<0軸上的一定點(diǎn)，若是，求出定點(diǎn)的坐標(biāo)；若不是，說明理由.題型五：直線相關(guān)的對(duì)稱問題一、單選題1．（2022·全國·高三專題練習(xí)（理））集合SKIPIF1<0在平面直角坐標(biāo)系中表示線段的長度之和記為SKIPIF1<0.若集合SKIPIF1<0，SKIPIF1<0，SKIPIF1<0則下列說法中不正確的有（

）A．若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為SKIPIF1<0 B．存在SKIPIF1<0，使SKIPIF1<0C．無論SKIPIF1<0取何值，都有SKIPIF1<0 D．SKIPIF1<0的最大值為SKIPIF1<02．（2022·全國·高三專題練習(xí)）已知平面向量SKIPIF1<0.若對(duì)區(qū)間SKIPIF1<0內(nèi)的三個(gè)任意的實(shí)數(shù)SKIPIF1<0,都有SKIPIF1<0,則向量SKIPIF1<0與SKIPIF1<0夾角的最大值的余弦值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題3．（2022·全國·模擬預(yù)測(cè)）已知直線SKIPIF1<0，過直線上任意一點(diǎn)M作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為A，B，則有（

）A．四邊形MACB面積的最小值為SKIPIF1<0 B．SKIPIF1<0最大度數(shù)為60°C．直線AB過定點(diǎn)SKIPIF1<0 D．SKIPIF1<0的最小值為SKIPIF1<04．（2022·福建三明·模擬預(yù)測(cè)）已知直線l：SKIPIF1<0與圓C：SKIPIF1<0相交于A，B兩點(diǎn)，O為坐標(biāo)原點(diǎn)，下列說法正確的是（

）A．SKIPIF1<0的最小值為SKIPIF1<0 B．若圓C關(guān)于直線l對(duì)稱，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0或SKIPIF1<0 D．若A，B，C，O四點(diǎn)共圓，則SKIPIF1<0三、填空題5．（2022·全國·模擬預(yù)測(cè)）已知平面內(nèi)點(diǎn)SKIPIF1<0，SKIPIF1<0SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0．設(shè)SKIPIF1<0到直線SKIPIF1<0的距離的最大值為SKIPIF1<0，若數(shù)列SKIPIF1<0的前n項(xiàng)和SKIPIF1<0恒成立，則實(shí)數(shù)m能取的最小值是______．6．（2022·天津·南開中學(xué)模擬預(yù)測(cè)）已知圓SKIPIF1<0和圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0與直線SKIPIF1<0平行，且與圓SKIPIF1<0相切，與圓SKIPIF1<0交于點(diǎn)SKIPIF1<0，則SKIPIF1<0__________．7．（2022·廣東佛山·模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則點(diǎn)P到直線l：SKIPIF1<0的距離的最小值為____________．四、解答題8．（2022·安徽·蚌埠二中模擬預(yù)測(cè)（理））在直角坐標(biāo)系xOy中，曲線C的參數(shù)方程為SKIPIF1<0(t為參數(shù))．(1)求C與坐標(biāo)軸交點(diǎn)的直角坐標(biāo)；(2)以坐標(biāo)原點(diǎn)O為極點(diǎn)，x軸非負(fù)半軸為極軸建立極坐標(biāo)系，曲線C與坐標(biāo)軸的交點(diǎn)是否共圓，若共圓，求出該圓的極坐標(biāo)方程；若不共圓，請(qǐng)說明理由.9．（2022·安徽·壽縣第一中學(xué)高三階段練習(xí)（理））已知直線SKIPIF1<0，圓SKIPIF1<0，圓SKIPIF1<0(1)若SKIPIF1<0，求直線SKIPIF1<0的傾斜角；(2)設(shè)直線SKIPIF1<0截兩圓的弦長分別為SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的最大值并求此時(shí)SKIPIF1<0的值.10．（2022·江西南昌·一模（理））已知面積為SKIPIF1<0的等邊SKIPIF1<0（SKIPIF1<0是坐標(biāo)原點(diǎn)）的三個(gè)頂點(diǎn)都在拋物線SKIPIF1<0上，過點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的兩條切線分別交SKIPIF1<0軸于SKIPIF1<0，SKIPIF1<0兩點(diǎn).(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的外接圓的方程.題型六：幾何法求圓的方程一、多選題1．（2022·廣東·模擬預(yù)測(cè)）三角形的外心、重心、垂心所在的直線稱為歐拉線．已知圓SKIPIF1<0的圓心在SKIPIF1<0的歐拉線SKIPIF1<0上，SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，且滿足SKIPIF1<0，則下列說法正確的是（

）A．圓SKIPIF1<0的方程為SKIPIF1<0B．SKIPIF1<0的方程為SKIPIF1<0C．圓SKIPIF1<0上的點(diǎn)到SKIPIF1<0的最大距離為SKIPIF1<0D．若點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0的取值范圍是SKIPIF1<0二、填空題2．（2022·河北·模擬預(yù)測(cè)）圓心為SKIPIF1<0，且截直線SKIPIF1<0所得弦長為SKIPIF1<0的圓的方程為___________.3．（2022·河南·高三階段練習(xí)（文））已知?圓SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，SKIPIF1<0和SKIPIF1<0是SKIPIF1<0的左右焦點(diǎn)，M是SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)N在線段SKIPIF1<0的延長線上，SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為P，則SKIPIF1<0的最大值為______．4．（2022·天津·高三專題練習(xí)）已知圓C過點(diǎn)SKIPIF1<0兩點(diǎn)，且圓心C在x軸上，經(jīng)過點(diǎn)SKIPIF1<0且傾斜角為鈍角的直線l交圓C于A，B兩點(diǎn)，若SKIPIF1<0(C為圓心)，則該直線l的斜率為________．5．（2022·全國·高三專題練習(xí)）已知圓C：(x－2)2＋y2＝2，直線l：y＝k(x＋2)與x軸交于點(diǎn)A，過l上一點(diǎn)P作圓C的切線，切點(diǎn)為T，若|PA|＝SKIPIF1<0|PT|，則實(shí)數(shù)k的取值范圍是______________．三、解答題6．（2022·內(nèi)蒙古呼和浩特·二模（理））拋物線C的頂點(diǎn)為坐標(biāo)原點(diǎn)O，焦點(diǎn)在x軸上，直線l：SKIPIF1<0交C于P，Q兩點(diǎn)，且SKIPIF1<0．已知點(diǎn)M的坐標(biāo)為SKIPIF1<0，SKIPIF1<0與直線l相切．(1)求拋物線C和SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)已知點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0是C上的兩個(gè)點(diǎn)，且直線SKIPIF1<0，SKIPIF1<0均與SKIPIF1<0相切．判斷直線SKIPIF1<0與SKIPIF1<0的位置關(guān)系，并說明理由．7．（2022·江蘇·南京市第五高級(jí)中學(xué)一模）已知O為坐標(biāo)原點(diǎn)，拋物線E：SKIPIF1<0（p＞0），過點(diǎn)C（0，2）作直線l交拋物線E于點(diǎn)A、B（其中點(diǎn)A在第一象限），SKIPIF1<0且SKIPIF1<0（SKIPIF1<0＞0）.(1)求拋物線E的方程；(2)當(dāng)SKIPIF1<0=2時(shí)，過點(diǎn)A、B的圓與拋物線E在點(diǎn)A處有共同的切線，求該圓的方程8．（2022·全國·高三專題練習(xí)）已知平面直角坐標(biāo)系上一動(dòng)點(diǎn)SKIPIF1<0到點(diǎn)SKIPIF1<0的距離是點(diǎn)SKIPIF1<0到點(diǎn)SKIPIF1<0的距離的SKIPIF1<0倍．（1）求點(diǎn)SKIPIF1<0的軌跡方程：（2）若點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，求SKIPIF1<0、SKIPIF1<0兩點(diǎn)間距離的最大值；（3）若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0，則是否存在直線SKIPIF1<0，使SKIPIF1<0取得最大值，若存在，求出此時(shí)的方程，若不存在，請(qǐng)說明理由．題型七：待定系數(shù)法求圓的方程一、單選題1．（2016·天津市紅橋區(qū)教師發(fā)展中心高三學(xué)業(yè)考試）已知圓SKIPIF1<0的半徑為1，若此圓同時(shí)與SKIPIF1<0軸和直線SKIPIF1<0相切，則圓SKIPIF1<0的標(biāo)準(zhǔn)方程可能是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、填空題2．（2022·四川眉山·三模（文））已知函數(shù)SKIPIF1<0.過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0兩條切線，兩切線與曲線SKIPIF1<0另外的公共點(diǎn)分別為B、C，則SKIPIF1<0外接圓的方程為___________.3．（2022·安徽·高三階段練習(xí)（文））已知拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的兩條切線SKIPIF1<0，SKIPIF1<0，切點(diǎn)分別為點(diǎn)A，B，以SKIPIF1<0為直徑的圓交x軸于P，Q兩點(diǎn)，則SKIPIF1<0_______．4．（2022·天津·高三專題練習(xí)）已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，拋物線SKIPIF1<0上一點(diǎn)SKIPIF1<0位于第一象限，且滿足SKIPIF1<0，則以點(diǎn)SKIPIF1<0為圓心，SKIPIF1<0為半徑的圓的方程為______.三、解答題5．（2022·全國·高三專題練習(xí)）已知圓C經(jīng)過點(diǎn)A(0，2)，B(2，0)，圓C的圓心在圓x2＋y2＝2的內(nèi)部，且直線3x＋4y＋5＝0被圓C所截得的弦長為SKIPIF1<0.點(diǎn)P為圓C上異于A，B的任意一點(diǎn)，直線PA與x軸交于點(diǎn)M，直線PB與y軸交于點(diǎn)N.(1)求圓C的方程；(2)若直線y＝x＋1與圓C交于A1，A2兩點(diǎn)，求SKIPIF1<0；(3)求證：|AN|·|BM|為定值.6．（2021·江西·高三階段練習(xí)（理））已知圓SKIPIF1<0過點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．(1)求SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)若點(diǎn)SKIPIF1<0在SKIPIF1<0上運(yùn)動(dòng)，求SKIPIF1<0的取值范圍．7．（2021·全國·模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0：SKIPIF1<0上，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0：SKIPIF1<0的兩條切線，切點(diǎn)為SKIPIF1<0，SKIPIF1<0，延長SKIPIF1<0，SKIPIF1<0交拋物線于SKIPIF1<0，SKIPIF1<0.（1）當(dāng)直線SKIPIF1<0拋物線焦點(diǎn)時(shí)，求拋物線SKIPIF1<0的方程與圓SKIPIF1<0的方程；（2）證明：對(duì)于任意SKIPIF1<0，直線SKIPIF1<0恒過定點(diǎn).8．（2019·云南·二模（理））已知SKIPIF1<0是坐標(biāo)原點(diǎn)，拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0且斜率為1的直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0為拋物線SKIPIF1<0的準(zhǔn)線上一點(diǎn)，且SKIPIF1<0.（1）求SKIPIF1<0點(diǎn)的坐標(biāo)；（2）設(shè)與直線SKIPIF1<0垂直的直線與拋物線SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，過點(diǎn)SKIPIF1<0、SKIPIF1<0分別作拋物線SKIPIF1<0的切線SKIPIF1<0、SKIPIF1<0，設(shè)直線SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0，若SKIPIF1<0，求SKIPIF1<0外接圓的標(biāo)準(zhǔn)方程.題型八：幾何法求弦長一、單選題1．（2022·全國·模擬預(yù)測(cè)）已知直線l過點(diǎn)SKIPIF1<0，則直線l被圓O：SKIPIF1<0截得的弦長的最小值為（

）A．3 B．6 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·模擬預(yù)測(cè)）過點(diǎn)SKIPIF1<0，作傾斜角為SKIPIF1<0的直線l，則直線l被圓SKIPIF1<0截得的弦長為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題3．（2022·廣東·模擬預(yù)測(cè)）已知圓SKIPIF1<0和圓SKIPIF1<0，過圓SKIPIF1<0上任意一點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，設(shè)兩切點(diǎn)分別為SKIPIF1<0，則（

）A．線段SKIPIF1<0的長度大于SKIPIF1<0B．線段SKIPIF1<0的長度小于SKIPIF1<0C．當(dāng)直線SKIPIF1<0與圓SKIPIF1<0相切時(shí)，原點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0D．當(dāng)直線SKIPIF1<0平分圓SKIPIF1<0的周長時(shí)，原點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0三、填空題4．（2022·河北唐山·三模）直線SKIPIF1<0與圓SKIPIF1<0交于A、B兩點(diǎn)，且SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0_______．四、解答題5．（2022·全國·高三專題練習(xí)）已知點(diǎn)SKIPIF1<0，不垂直于x軸的直線l與橢圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).(1)若M為線段AB的中點(diǎn)，證明：SKIPIF1<0；(2)設(shè)C的左焦點(diǎn)為F，若M在∠AFB的角平分線所在直線上，且l被圓SKIPIF1<0截得的弦長為SKIPIF1<0，求l的方程.6．（2021·湖北·武漢市第六中學(xué)高三階段練習(xí)）已知圓O：x2＋y2=2，過點(diǎn)A（1，1）的直線交圓O所得的弦長為SKIPIF1<0，且與x軸的交點(diǎn)為雙曲線E：SKIPIF1<0=1的右焦點(diǎn)F（c，0）（c＞2），雙曲線E的離心率為SKIPIF1<0．(1)求雙曲線E的方程；(2)若直線y=kx＋m（k＜0，k≠﹣SKIPIF1<0，m＞0）交y軸于點(diǎn)P