新高考數(shù)學(xué)一輪復(fù)習(xí)分層提升練習(xí)第45練 拋物線及其性質(zhì)（原卷版）

第45練拋物線及其性質(zhì)（精練）刷真題明導(dǎo)向刷真題明導(dǎo)向一、單選題1．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上．若SKIPIF1<0到直線SKIPIF1<0的距離為5，則SKIPIF1<0（

）A．7 B．6 C．5 D．42．設(shè)F為拋物線SKIPIF1<0的焦點(diǎn)，點(diǎn)A在C上，點(diǎn)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．2 B．SKIPIF1<0 C．3 D．SKIPIF1<03．拋物線SKIPIF1<0的焦點(diǎn)到直線SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．SKIPIF1<0 D．4二、填空題4．已知點(diǎn)SKIPIF1<0在拋物線C：SKIPIF1<0上，則A到C的準(zhǔn)線的距離為.三、雙空題5．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軸與于點(diǎn)SKIPIF1<0.若SKIPIF1<0，則點(diǎn)SKIPIF1<0的橫坐標(biāo)為；SKIPIF1<0的面積為．【A組

】一、單選題1．兩拋物線SKIPIF1<0與SKIPIF1<0的焦點(diǎn)間的距離為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．拋物線SKIPIF1<0的準(zhǔn)線方程是SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值（

）A．SKIPIF1<0 B．SKIPIF1<0 C．8 D．SKIPIF1<03．拋物線SKIPIF1<0的焦點(diǎn)坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．石拱橋是世界橋梁史上出現(xiàn)較早、形式優(yōu)美、結(jié)構(gòu)堅(jiān)固的一種橋型.如圖，這是一座石拱橋，橋洞弧線可近似看成是頂點(diǎn)在坐標(biāo)原點(diǎn)，焦點(diǎn)在y軸負(fù)半軸上的拋物線C的一部分，當(dāng)水距離拱頂4米時(shí)，水面的寬度是8米，則拋物線C的焦點(diǎn)到準(zhǔn)線的距離是（

）

A．1米 B．2米 C．4米 D．8米5．焦點(diǎn)坐標(biāo)為SKIPIF1<0的拋物線的標(biāo)準(zhǔn)方程是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上．若SKIPIF1<0到直線SKIPIF1<0的距離為3，則SKIPIF1<0（

）A．4 B．5 C．6 D．77．拋物線SKIPIF1<0的焦點(diǎn)到圓SKIPIF1<0上點(diǎn)的距離的最大值為（

）A．6 B．2 C．5 D．88．已知拋物線的焦點(diǎn)在SKIPIF1<0軸上，且焦點(diǎn)到坐標(biāo)原點(diǎn)的距離為1，則拋物線的標(biāo)準(zhǔn)方程為（

）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<09．已知圓SKIPIF1<0與拋物線SKIPIF1<0的準(zhǔn)線相切，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．8 D．210．O為坐標(biāo)原點(diǎn)，F(xiàn)為拋物線SKIPIF1<0的焦點(diǎn)，M為C上一點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．811．已知拋物線C：SKIPIF1<0的頂點(diǎn)為O，經(jīng)過點(diǎn)SKIPIF1<0，且F為拋物線C的焦點(diǎn)，若SKIPIF1<0，則p＝（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．212．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，拋物線SKIPIF1<0上有一動(dòng)點(diǎn)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．8 B．16 C．11 D．2613．過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0且傾斜角為銳角的直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，過線段SKIPIF1<0的中點(diǎn)SKIPIF1<0且垂直于SKIPIF1<0的直線與SKIPIF1<0的準(zhǔn)線交于點(diǎn)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的斜率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．214．設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，過第一象限內(nèi)的拋物線上一點(diǎn)SKIPIF1<0作SKIPIF1<0的垂線，垂足為SKIPIF1<0，設(shè)SKIPIF1<0，且SKIPIF1<0為等邊三角形，SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．215．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0的直線交拋物線于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的中點(diǎn)到準(zhǔn)線的距離為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，圓SKIPIF1<0（SKIPIF1<0）經(jīng)過點(diǎn)F，且圓心SKIPIF1<0在拋物線上，則實(shí)數(shù)SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．已知拋物線SKIPIF1<0的焦點(diǎn)為F，點(diǎn)P在C上，若點(diǎn)SKIPIF1<0，則SKIPIF1<0周長(zhǎng)的最小值為（

）．A．13 B．12 C．10 D．8【答案】A18．已知F為拋物線SKIPIF1<0的焦點(diǎn)，P為該拋物線上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<0二、多選題19．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，若SKIPIF1<0為坐標(biāo)原點(diǎn)，則（

）A．點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<020．已知拋物線C：SKIPIF1<0的焦點(diǎn)為F，其準(zhǔn)線l與x軸交于點(diǎn)P，過C上一點(diǎn)M作l的垂線，垂足為Q，若四邊形MQPF為矩形，則（

）A．準(zhǔn)線l的方程為SKIPIF1<0 B．矩形MQPF為正方形C．點(diǎn)M的坐標(biāo)為SKIPIF1<0 D．點(diǎn)M到原點(diǎn)O的距離為SKIPIF1<021．（多選）設(shè)斜率為2的直線l過拋物線SKIPIF1<0的焦點(diǎn)F，且和y軸交于點(diǎn)A，若SKIPIF1<0（O為坐標(biāo)原點(diǎn)）的面積為4，則拋物線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<022．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，頂點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，若SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<023．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<024．設(shè)拋物線SKIPIF1<0，SKIPIF1<0為其焦點(diǎn)，SKIPIF1<0為拋物線上一點(diǎn).則下列結(jié)論正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0點(diǎn)到焦點(diǎn)的距離為3，則SKIPIF1<0的坐標(biāo)為SKIPIF1<0.C．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<0.D．過焦點(diǎn)SKIPIF1<0作斜率為2的直線與拋物線相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<025．已知拋物線C：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0點(diǎn)SKIPIF1<0在SKIPIF1<0上，且弦SKIPIF1<0的中點(diǎn)到直線SKIPIF1<0的距離為5，則（

）A．SKIPIF1<0 B．線段SKIPIF1<0的長(zhǎng)為定值C．SKIPIF1<0兩點(diǎn)到SKIPIF1<0的準(zhǔn)線的距離之和為14 D．SKIPIF1<0的最大值為4926．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，記坐標(biāo)原點(diǎn)為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<027．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，下列說法正確的是（

）A．SKIPIF1<0的準(zhǔn)線方程為SKIPIF1<0B．直線SKIPIF1<0與SKIPIF1<0相切C．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0的周長(zhǎng)的最小值為1128．已知雙曲線SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，拋物線SKIPIF1<0的焦點(diǎn)與雙曲線C的一個(gè)焦點(diǎn)重合，點(diǎn)P是這兩條曲線的一個(gè)公共點(diǎn)，則下列說法正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0的周長(zhǎng)為16C．SKIPIF1<0的面積為SKIPIF1<0 D．SKIPIF1<0三、填空題29．已知拋物線SKIPIF1<0上有一動(dòng)點(diǎn)SKIPIF1<0，則SKIPIF1<0與點(diǎn)SKIPIF1<0距離的最小值為．30．設(shè)拋物線SKIPIF1<0（SKIPIF1<0）的準(zhǔn)線與直線SKIPIF1<0的距離為3，則拋物線的標(biāo)準(zhǔn)方程為．31．若拋物線SKIPIF1<0上一點(diǎn)SKIPIF1<0到焦點(diǎn)的距離是該點(diǎn)到SKIPIF1<0軸距離的SKIPIF1<0倍，則SKIPIF1<0.32．已知拋物線SKIPIF1<0上的點(diǎn)到準(zhǔn)線的最小距離為SKIPIF1<0，則拋物線的焦點(diǎn)坐標(biāo)為．33．已知拋物線C的方程為SKIPIF1<0，若傾斜角為銳角的直線l過拋物線的焦點(diǎn)F，與拋物線交于A，B兩點(diǎn)，且SKIPIF1<0，則直線l的傾斜角為．34．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，設(shè)點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，若以線段SKIPIF1<0為直徑的圓過點(diǎn)SKIPIF1<0，則SKIPIF1<0.35．已知拋物線SKIPIF1<0的準(zhǔn)線為SKIPIF1<0，圓SKIPIF1<0與SKIPIF1<0相切，則拋物線SKIPIF1<0的焦點(diǎn)坐標(biāo)為.36．設(shè)SKIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，SKIPIF1<0是拋物線上的兩點(diǎn)，線段SKIPIF1<0的中點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為．37．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0上一點(diǎn)SKIPIF1<0作SKIPIF1<0的準(zhǔn)線SKIPIF1<0的垂線，垂足為SKIPIF1<0，若直線SKIPIF1<0的斜率為-2，則SKIPIF1<0的面積為.38．已知拋物SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線為l，點(diǎn)P在C上，直線PF交y軸于點(diǎn)Q，若SKIPIF1<0，則P到準(zhǔn)線l的距離為.39．已知拋物線SKIPIF1<0的SKIPIF1<0的準(zhǔn)線與SKIPIF1<0軸交于SKIPIF1<0點(diǎn)，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的焦點(diǎn)，SKIPIF1<0是SKIPIF1<0上一點(diǎn)，SKIPIF1<0，則SKIPIF1<0.40．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線上一點(diǎn)，且SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），SKIPIF1<0，垂足為SKIPIF1<0，則SKIPIF1<0的面積是.【B組】一、單選題1．如圖，太陽灶是一種將太陽光反射至一點(diǎn)用來加熱水或食物的設(shè)備，上面裝有拋物面形的反光鏡，鏡的軸截面是拋物線的一部分，已知太陽灶的口徑（直徑）為4m，深度為0.5m，則該拋物線頂點(diǎn)到焦點(diǎn)的距離為（

）

A．0.25m B．0.5m C．1m D．2m2．設(shè)O為坐標(biāo)原點(diǎn)，F(xiàn)為拋物線C：SKIPIF1<0的焦點(diǎn)，直線SKIPIF1<0與拋物線C交于A，B兩點(diǎn)，若SKIPIF1<0，則拋物線C的準(zhǔn)線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<03．若點(diǎn)SKIPIF1<0在焦點(diǎn)為SKIPIF1<0的拋物線SKIPIF1<0上，且SKIPIF1<0，點(diǎn)SKIPIF1<0為直線SKIPIF1<0上的動(dòng)點(diǎn)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．44．拋物線SKIPIF1<0的頂點(diǎn)為原點(diǎn)，焦點(diǎn)為SKIPIF1<0，則點(diǎn)SKIPIF1<0到拋物線SKIPIF1<0上動(dòng)點(diǎn)SKIPIF1<0的距離最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知拋物線SKIPIF1<0的頂點(diǎn)為O，焦點(diǎn)為F，準(zhǔn)線為直線l，點(diǎn)E在拋物線上．若E在直線l上的射影為Q，且Q在第四象限，SKIPIF1<0，則直線FE的傾斜角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<06．已知拋物線SKIPIF1<0的焦點(diǎn)為F，點(diǎn)SKIPIF1<0，若點(diǎn)A為拋物線任意一點(diǎn)，當(dāng)SKIPIF1<0取最小值時(shí)，點(diǎn)A的坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，SKIPIF1<0于SKIPIF1<0.若SKIPIF1<0，則拋物線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．直線SKIPIF1<0經(jīng)過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，且與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．若SKIPIF1<0，則SKIPIF1<0（

）A．4 B．SKIPIF1<0 C．8 D．SKIPIF1<09．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0，線段SKIPIF1<0與拋物線SKIPIF1<0相交于點(diǎn)SKIPIF1<0，若拋物線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與直線SKIPIF1<0垂直，則拋物線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0為拋物線上一點(diǎn)，過點(diǎn)SKIPIF1<0作拋物線的準(zhǔn)線的垂線，垂足為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0（

）A．2 B．8 C．SKIPIF1<0 D．411．過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若直線SKIPIF1<0過點(diǎn)SKIPIF1<0，且SKIPIF1<0，則拋物線SKIPIF1<0的準(zhǔn)線方程是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知拋物線SKIPIF1<0上三點(diǎn)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，直線SKIPIF1<0、SKIPIF1<0是圓SKIPIF1<0的兩條切線，則直線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．在平面直角坐標(biāo)系SKIPIF1<0中，拋物線SKIPIF1<0為SKIPIF1<0軸正半軸上一點(diǎn)，線段SKIPIF1<0的垂直平分線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則四邊形SKIPIF1<0的周長(zhǎng)為（

）A．SKIPIF1<0 B．64 C．SKIPIF1<0 D．8014．已知拋物線SKIPIF1<0，F(xiàn)為拋物線的焦點(diǎn)，P為拋物線上一點(diǎn)，過點(diǎn)P作PQ垂直于拋物線的準(zhǔn)線，垂足為Q，若SKIPIF1<0，則△PFQ的面積為（

）A．4 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0且傾斜角為SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0上的動(dòng)點(diǎn)，且點(diǎn)SKIPIF1<0在SKIPIF1<0的右下方，則SKIPIF1<0面積的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．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<0二、多選題17．直線SKIPIF1<0與拋物線SKIPIF1<0相交于A?B兩點(diǎn)，下列說法正確的是（

）A．拋物線C的焦點(diǎn)是SKIPIF1<0 B．拋物線C的準(zhǔn)線方程為SKIPIF1<0C．SKIPIF1<0 D．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<018．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，頂點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，若SKIPIF1<0，則下列選項(xiàng)正確的是（

）A．SKIPIF1<0 B．以MF為直徑的圓與SKIPIF1<0軸相切C．SKIPIF1<0 D．SKIPIF1<019．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)SKIPIF1<0到準(zhǔn)線的距離為2，過點(diǎn)SKIPIF1<0的直線與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，則下列結(jié)論正確的是（

）A．此拋物線上與焦點(diǎn)SKIPIF1<0的距離等于3的點(diǎn)的坐標(biāo)是SKIPIF1<0B．若SKIPIF1<0，則點(diǎn)SKIPIF1<0到SKIPIF1<0軸的距離為3C．SKIPIF1<0是準(zhǔn)線上一點(diǎn)，SKIPIF1<0是直線SKIPIF1<0與SKIPIF1<0的一個(gè)交點(diǎn)，若SKIPIF1<0，則SKIPIF1<0D．SKIPIF1<020．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)，SKIPIF1<0于SKIPIF1<0，則下列說法正確的是（

）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21．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<022．設(shè)拋物線SKIPIF1<0的頂點(diǎn)為O，焦點(diǎn)為F.點(diǎn)M是拋物線上異于O的一動(dòng)點(diǎn)，直線OM交拋物線的準(zhǔn)線于點(diǎn)N，下列結(jié)論正確的是（

）A．若SKIPIF1<0，則O為線段MN的中點(diǎn) B．若SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0 D．存在點(diǎn)M，使得SKIPIF1<0三、填空題23．若動(dòng)點(diǎn)SKIPIF1<0到點(diǎn)SKIPIF1<0的距離比它到直線SKIPIF1<0的距離大1，則SKIPIF1<0的軌跡方程是．24．已知F是拋物線SKIPIF1<0的焦點(diǎn)，M是C上一點(diǎn)，F(xiàn)M的延長(zhǎng)線交y軸于點(diǎn)N，若SKIPIF1<0，則SKIPIF1<025．已知拋物線SKIPIF1<0的焦點(diǎn)F到準(zhǔn)線的距離為4，點(diǎn)SKIPIF1<0，SKIPIF1<0在拋物線C上，若SKIPIF1<0，則SKIPIF1<0.26．已知拋物線SKIPIF1<0(其中SKIPIF1<0)的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線上，若SKIPIF1<0，且SKIPIF1<0的最小值為SKIPIF1<0，則點(diǎn)SKIPIF1<0到拋物線SKIPIF1<0的準(zhǔn)線的距離為27．已知SKIPIF1<0為拋物線SKIPIF1<0上的動(dòng)點(diǎn)，SKIPIF1<0為拋物線的焦點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0周長(zhǎng)的最小值為.28．設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0垂直SKIPIF1<0軸，SKIPIF1<0，則SKIPIF1<0．29．已知點(diǎn)SKIPIF1<0分別是拋物線SKIPIF1<0和圓SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0的最小值為．30．已知點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0上任意一點(diǎn)，點(diǎn)SKIPIF1<0為圓SKIPIF1<0上任意一點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為.31．已知點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上運(yùn)動(dòng)，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)，則SKIPIF1<0的最小值.32．已知F是拋物線C：y2=4x的焦點(diǎn)，過點(diǎn)F的直線l與拋物線C交于A，B兩點(diǎn)，過AB的中點(diǎn)M作y軸的垂線與拋物線在第一象限內(nèi)交于點(diǎn)P，若SKIPIF1<0，則M點(diǎn)的橫坐標(biāo)為【C組

】一、單選題1．已知拋物線SKIPIF1<0過點(diǎn)SKIPIF1<0，其準(zhǔn)線與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與拋物線的另一個(gè)交點(diǎn)為SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，SKIPIF1<0是圓SKIPIF1<0關(guān)于直線SKIPIF1<0的對(duì)稱曲線SKIPIF1<0上一點(diǎn)，則SKIPIF1<0的最小值是A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．拋物線SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，圓心SKIPIF1<0，點(diǎn)SKIPIF1<0為劣弧SKIPIF1<0上不同于SKIPIF1<0、SKIPIF1<0的一個(gè)動(dòng)點(diǎn)，平行于SKIPIF1<0軸的直線SKIPIF1<0交拋物線于點(diǎn)SKIPIF1<0，則SKIPIF1<0的周長(zhǎng)的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0在拋物線SKIPIF1<0上，過線段SKIPIF1<0的中點(diǎn)SKIPIF1<0作拋物線SKIPIF1<0的準(zhǔn)線的垂線，垂足為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的最小值為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知拋物線SKIPIF1<0，圓SKIPIF1<0，若點(diǎn)SKIPIF1<0、SKIPIF1<0分別在SKIPIF1<0、SKIPIF1<0上運(yùn)動(dòng)，且設(shè)點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，其準(zhǔn)線與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線與此拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0（

）A．3 B．4 C．5 D．67．設(shè)拋物線SKIPIF1<0(SKIPIF1<0)的焦點(diǎn)為SKIPIF1<0,準(zhǔn)線為SKIPIF1<0,過焦點(diǎn)的直線分別交拋物線于SKIPIF1<0兩點(diǎn),分別過SKIPIF1<0作SKIPIF1<0的垂線,垂足為SKIPIF1<0.若SKIPIF1<0,且三角形SKIPIF1<0的面積為SKIPIF1<0,則SKIPIF1<0的值為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．如圖所示，已知拋物線SKIPIF1<0過點(diǎn)SKIPIF1<0，圓SKIPIF1<0.過圓心SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0和圓SKIPIF1<0分別交于SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知拋物線SKIPIF1<0，焦點(diǎn)為F，點(diǎn)M是拋物線C上的動(dòng)點(diǎn)，過點(diǎn)F作直線SKIPIF1<0的垂線，垂足為P，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．310．已知點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）上的動(dòng)點(diǎn)，若SKIPIF1<0的最小值為1，則拋物線SKIPIF1<0的準(zhǔn)線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．拋物線SKIPIF1<0的焦點(diǎn)為F，點(diǎn)SKIPIF1<0為該拋物線上的動(dòng)點(diǎn)，點(diǎn)A是拋物線的準(zhǔn)線與坐標(biāo)軸的交點(diǎn)，則SKIPIF1<0的最大值是（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0，直線SKIPIF1<0與拋物線SKIPIF1<0交于點(diǎn)SKIPIF1<0（SKIPIF1<0在第一象限內(nèi))，與其準(zhǔn)線交于點(diǎn)SKIPIF1<0，若SKIPIF1<0，則點(diǎn)SKIPIF1<0到SKIPIF1<0軸距離為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題13．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過焦點(diǎn)SKIPIF1<0的直線交拋物線于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，若SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0 B．直線SKIPIF1<0的斜率為SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．已知拋物線C：SKIPIF1<0與圓O：SKIPIF1<0交于A，B兩點(diǎn)，且SKIPIF1<0，直線SKIPIF1<0過C的焦點(diǎn)F，且與C交于M，N兩點(diǎn)，則下列說法中正確的是（

）A．若直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0B．SKIPIF1<0的最小值為SKIPIF1<0C．若以MF為直徑的圓與y軸的公共點(diǎn)為SKIPIF1<0，則點(diǎn)M的橫坐標(biāo)為SKIPIF1<0D．若點(diǎn)SKIPIF1<0，則SKIPIF1<0周長(zhǎng)的最小值為SKIPIF1<015．如圖所示，拋物線E：SKIPIF1<0的焦點(diǎn)為F，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0，SKIPIF1<0與E分別相交于SKIPIF1<0，SKIPIF1<0和C，D兩點(diǎn)，直線AD經(jīng)過點(diǎn)F，當(dāng)直線AB垂直于x軸時(shí)，SKIPIF1<0．下列結(jié)論正確的是（

）A．E的方程為SKIPIF1<0B．SKIPIF1<0C．若AD，BC的斜率分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0D．若AD，BC的傾斜角分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最大值為SKIPIF1<016．設(shè)O為坐標(biāo)原點(diǎn)，F(xiàn)為拋物線C：SKIPIF1<0的焦點(diǎn)，過焦點(diǎn)F且傾斜角為SKIPIF1<0的直線SKIPIF1<0與拋物線C交于M，N兩點(diǎn)（點(diǎn)M在第二象限），當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0B．△MON的面積的最小值為SKIPIF1<0C．存在直線SKIPIF1<0，使得SKIPIF1<0D．分別過點(diǎn)M，N且與拋物線相切的兩條直線互相垂直17．已知拋物線SKIPIF1<0上三點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，F(xiàn)為拋物線的焦點(diǎn)，則下列結(jié)論正確的是（

）A．拋物線的準(zhǔn)線l的方程為SKIPIF1<0B．若F為SKIPIF