新高考數(shù)學(xué)一輪復(fù)習(xí)講練測第8章第07講 拋物線及其性質(zhì)（練習(xí)）（原卷版）

第07講拋物線及其性質(zhì)（模擬精練+真題演練）1．（2023·四川成都·校聯(lián)考二模）已知點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0上任意一點(diǎn)，則SKIPIF1<0的最小值為（

）A．5 B．6 C．7 D．82．（2023·陜西西安·西安市第三十八中學(xué)?？寄M預(yù)測）若拋物線SKIPIF1<0（SKIPIF1<0）上一點(diǎn)SKIPIF1<0到焦點(diǎn)的距離是SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·四川成都·校聯(lián)考模擬預(yù)測）已知點(diǎn)SKIPIF1<0是拋物線C：SKIPIF1<0的焦點(diǎn)，點(diǎn)M在拋物線C上，點(diǎn)SKIPIF1<0，且SKIPIF1<0，則點(diǎn)M到y(tǒng)軸的距離為（

）A．6 B．8 C．10 D．124．（2023·四川綿陽·統(tǒng)考二模）涪江三橋又名綿陽富樂大橋，跨越了涪江和芙蓉溪，是繼東方紅大橋、涪江二橋之后在涪江上修建的第三座大橋，于2004年國慶全線通車．大橋的拱頂可近似地看作拋物線SKIPIF1<0的一段，若有一只鴿子站在拱頂?shù)哪硞€(gè)位置，它到拋物線焦點(diǎn)的距離為10米，則鴿子到拱頂?shù)淖罡唿c(diǎn)的距離為（

）A．6 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·全國·模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線為l，與x軸平行的直線與l和拋物線C分別交于A，B兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．46．（2023·海南·海南中學(xué)?？寄M預(yù)測）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和SKIPIF1<0距離之和的最小值是（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．37．（2023·河南·校聯(lián)考二模）設(shè)F為拋物線SKIPIF1<0的焦點(diǎn)，點(diǎn)M在C上，點(diǎn)N在準(zhǔn)線l上，且SKIPIF1<0平行于x軸，準(zhǔn)線l與x軸的交點(diǎn)為E，若SKIPIF1<0，則梯形SKIPIF1<0的面積為（

）A．12 B．6 C．SKIPIF1<0 D．SKIPIF1<08．（2023·江西贛州·統(tǒng)考模擬預(yù)測）已知過拋物線C：SKIPIF1<0的焦點(diǎn)SKIPIF1<0的直線與拋物線C交于A，B兩點(diǎn)（A在第一象限），以AB為直徑的圓E與拋物線C的準(zhǔn)線相切于點(diǎn)D．若SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．49．（2023·福建廈門·廈門雙十中學(xué)校考模擬預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0在SKIPIF1<0上，圓SKIPIF1<0的半徑為1，過點(diǎn)SKIPIF1<0的直線與圓SKIPIF1<0相切于點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．2 B．3 C．4 D．510．（2023·河南·統(tǒng)考三模）已知拋物線SKIPIF1<0的準(zhǔn)線為SKIPIF1<0，焦點(diǎn)為F，過點(diǎn)F的直線與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，點(diǎn)P在l上的射影為SKIPIF1<0，則下列結(jié)論錯(cuò)誤的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．以PQ為直徑的圓與準(zhǔn)線l相切C．設(shè)SKIPIF1<0，則SKIPIF1<0D．過點(diǎn)SKIPIF1<0與拋物線C有且僅有一個(gè)公共點(diǎn)的直線至多有2條11．（多選題）（2023·湖南常德·常德市一中?？寄M預(yù)測）已知拋物線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，其焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線交于點(diǎn)SKIPIF1<0，SKIPIF1<0，設(shè)直線SKIPIF1<0，SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．（多選題）（2023·海南?？凇ずＤ先A僑中學(xué)?？寄M預(yù)測）設(shè)SKIPIF1<0為拋物線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）的焦點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0，則（

）A．SKIPIF1<0B．SKIPIF1<0C．直線SKIPIF1<0的斜率為SKIPIF1<0D．SKIPIF1<0的面積為SKIPIF1<013．（多選題）（2023·云南昭通·校聯(lián)考模擬預(yù)測）已知A，B是拋物線SKIPIF1<0：SKIPIF1<0上兩動(dòng)點(diǎn)，SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，則（

）A．直線AB過焦點(diǎn)F時(shí)，SKIPIF1<0最小值為4B．直線AB過焦點(diǎn)F且傾斜角為SKIPIF1<0時(shí)，SKIPIF1<0C．若AB中點(diǎn)M的橫坐標(biāo)為2，則SKIPIF1<0最大值為5D．SKIPIF1<014．（多選題）（2023·福建福州·福州四中?？寄M預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0為SKIPIF1<0的準(zhǔn)線與SKIPIF1<0軸的交點(diǎn)，若直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則下列結(jié)論正確的為（

）A．SKIPIF1<0B．存在唯一實(shí)數(shù)SKIPIF1<0，使得直線SKIPIF1<0與SKIPIF1<0相切C．恰有2個(gè)實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立D．恰有2個(gè)實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立15．（多選題）（2023·福建福州·福建省福州第一中學(xué)校考模擬預(yù)測）拋物線有如下光學(xué)性質(zhì)：從焦點(diǎn)發(fā)出的光線經(jīng)拋物線反射后，沿平行于拋物線對(duì)稱軸的方向射出；反之，平行于拋物線對(duì)稱軸的入射光線經(jīng)拋物線反射后，必過拋物線的焦點(diǎn).已知平行于SKIPIF1<0軸的光線SKIPIF1<0從點(diǎn)SKIPIF1<0射入，經(jīng)過拋物線SKIPIF1<0上的點(diǎn)SKIPIF1<0反射，再經(jīng)過SKIPIF1<0上另一點(diǎn)SKIPIF1<0反射后，沿直線SKIPIF1<0射出，經(jīng)過點(diǎn)SKIPIF1<0，則（

）

A．若SKIPIF1<0的方程為SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0的方程為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0C．分別延長SKIPIF1<0交于點(diǎn)SKIPIF1<0，則點(diǎn)SKIPIF1<0在SKIPIF1<0的準(zhǔn)線上D．拋物線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線分別與直線SKIPIF1<0，SKIPIF1<0所成角相等16．（多選題）（2023·湖南益陽·安化縣第二中學(xué)校考三模）已知直線SKIPIF1<0過拋物線C：SKIPIF1<0的焦點(diǎn)F，且與拋物線C交于A，B兩點(diǎn)，過A，B兩點(diǎn)分別作拋物線C的切線，兩切線交于點(diǎn)G，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列選項(xiàng)正確的是：（

）A．SKIPIF1<0B．以線段AB為直徑的圓與直線SKIPIF1<0相離C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0D．SKIPIF1<0面積的取值范圍為SKIPIF1<017．（2023·福建泉州·統(tǒng)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與SKIPIF1<0交于不同的兩點(diǎn)SKIPIF1<0，SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0.18．（2023·陜西咸陽·武功縣普集高級(jí)中學(xué)校考模擬預(yù)測）已知點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)SKIPIF1<0且傾斜角為SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0.19．（2023·上海虹口·華東師范大學(xué)第一附屬中學(xué)?？既＃┮阎猄KIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，P是拋物線C上一動(dòng)點(diǎn)，Q是曲線SKIPIF1<0上一動(dòng)點(diǎn)，則SKIPIF1<0的最小值為．20．（2023·甘肅隴南·統(tǒng)考一模）設(shè)SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為該拋物線上不同的三點(diǎn)，若SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則SKIPIF1<0.21．（2023·河北保定·河北省唐縣第一中學(xué)?？级＃┰谄矫嬷苯亲鴺?biāo)系SKIPIF1<0中，已知直線SKIPIF1<0（SKIPIF1<0），定點(diǎn)SKIPIF1<0與定直線SKIPIF1<0，過P向直線SKIPIF1<0作垂線，垂足為H．SKIPIF1<0，若動(dòng)點(diǎn)P的軌跡為曲線C，且直線SKIPIF1<0與曲線C相切，則SKIPIF1<0．22．（2023·廣東茂名·茂名市第一中學(xué)?？既＃┮阎猄KIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，與拋物線SKIPIF1<0及其準(zhǔn)線依次交于SKIPIF1<0三點(diǎn)（其中點(diǎn)SKIPIF1<0在SKIPIF1<0之間），若SKIPIF1<0.則SKIPIF1<0的面積是.23．（2023·上海嘉定·上海市嘉定區(qū)第一中學(xué)?？既＃┮阎c(diǎn)P是拋物線SKIPIF1<0上的動(dòng)點(diǎn)，Q是圓SKIPIF1<0上的動(dòng)點(diǎn)，則SKIPIF1<0的最大值是.24．（2023·福建莆田·?？寄M預(yù)測）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，SKIPIF1<0、SKIPIF1<0是SKIPIF1<0上異于點(diǎn)SKIPIF1<0的兩點(diǎn)（SKIPIF1<0為坐標(biāo)原點(diǎn)），若SKIPIF1<0，過SKIPIF1<0的中點(diǎn)SKIPIF1<0作SKIPIF1<0于點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為．1．（2020?新課標(biāo)Ⅲ）設(shè)SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的焦點(diǎn)坐標(biāo)為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2020?北京）設(shè)拋物線的頂點(diǎn)為SKIPIF1<0，焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0．SKIPIF1<0是拋物線上異于SKIPIF1<0的一點(diǎn)，過SKIPIF1<0作SKIPIF1<0于SKIPIF1<0，則線段SKIPIF1<0的垂直平分線SKIPIF1<0SKIPIF1<0A．經(jīng)過點(diǎn)SKIPIF1<0 B．經(jīng)過點(diǎn)SKIPIF1<0 C．平行于直線SKIPIF1<0 D．垂直于直線SKIPIF1<03．（多選題）（2023?新高考Ⅱ）設(shè)SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0過拋物線SKIPIF1<0的焦點(diǎn)，且與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0為SKIPIF1<0的準(zhǔn)線，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．以SKIPIF1<0為直徑的圓與SKIPIF1<0相切 D．SKIPIF1<0為等腰三角形4．（多選題）（2022?新高考Ⅱ）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，過拋物線SKIPIF1<0焦點(diǎn)SKIPIF1<0的直線與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，其中SKIPIF1<0在第一象限，點(diǎn)SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．直線SKIPIF1<0的斜率為SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（多選題）（2022?新高考Ⅰ）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0的準(zhǔn)線為SKIPIF1<0 B．直線SKIPIF1<0與SKIPIF1<0相切 C．SKIPIF1<0 D．SKIPIF1<06．（2023?乙卷）已知點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，則SKIPIF1<0到SKIPIF1<0的準(zhǔn)線的距離為．7．（2021?新高考Ⅰ）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，SKIPIF1<0與SKIPIF1<0軸垂直，SKIPIF1<0為SKIPIF1<0軸上一點(diǎn)，且SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0的準(zhǔn)線方程為．8．（2021?北京）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線上，SKIPIF1<0垂直SKIPIF1<0軸于點(diǎn)SKIPIF1<0，若SKIPIF1<0，則點(diǎn)SKIPIF1<0的橫坐標(biāo)是；SKIPIF1<0的面積為．9．（2021?全國）已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0傾斜角為SKIPIF1<0的直線與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0．10．（2021?上海）已知拋物線SKIPIF1<0，若第一象限的SKIPIF1<0，SKIPIF1<0在拋物線上，焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，求直線SKIPIF1<0的斜率為．11．（2020?海南）斜率為SKIPIF1<0的直線過拋物線SKIPIF1<0的焦點(diǎn)，且與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0．12．（2023?甲卷）設(shè)拋物線SKIPIF