新高考數(shù)學(xué)二輪復(fù)習(xí) 易錯(cuò)點(diǎn)18 拋物線(xiàn)（原卷版）

易錯(cuò)點(diǎn)18拋物線(xiàn)易錯(cuò)點(diǎn)1：主觀(guān)認(rèn)為拋物線(xiàn)的頂點(diǎn)就是原點(diǎn);易錯(cuò)點(diǎn)2：忽視拋物線(xiàn)的變化趨勢(shì),只從圖形的局部,亂下結(jié)論;易錯(cuò)點(diǎn)3：在使用拋物線(xiàn)的焦半徑公式時(shí),錯(cuò)把縱坐標(biāo)寫(xiě)成橫坐標(biāo);易錯(cuò)點(diǎn)4：解決直線(xiàn)與拋物線(xiàn)綜合題時(shí),忽略對(duì)直線(xiàn)斜率不存在情況的討論;易錯(cuò)點(diǎn)5：在解有關(guān)直線(xiàn)與拋物線(xiàn)的位置關(guān)系的問(wèn)題必記結(jié)論直線(xiàn)AB過(guò)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)，交拋物線(xiàn)于A(yíng)(x1，y1)，B(x2，y2)兩點(diǎn)，如圖：更多免費(fèi)資源，關(guān)注公眾號(hào)拾穗者的雜貨鋪（1）y1y2＝－p2，x1x2＝eq\f(p2,4).（2）|AB|＝x1＋x2＋p，x1＋x2≥SKIPIF1<0＝p，即當(dāng)x1＝x2時(shí)，弦長(zhǎng)最短為2p.（3）eq\f(1,|AF|)＋eq\f(1,|BF|)為定值eq\f(2,p).（4）弦長(zhǎng)AB＝eq\f(2p,sin2α)(α為AB的傾斜角)．（5）以AB為直徑的圓與準(zhǔn)線(xiàn)相切。（6）以AF為直徑的圓與y軸相切．（7）焦點(diǎn)F對(duì)A，B在準(zhǔn)線(xiàn)上射影的張角為90°.題組一：定義和標(biāo)準(zhǔn)方程1.（2021新高考2卷）拋物線(xiàn)SKIPIF1<0的焦點(diǎn)到直線(xiàn)SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0（）A.1 B.2 C.SKIPIF1<0 D.42.(2019年高考全國(guó)Ⅱ卷理數(shù))若拋物線(xiàn)的焦點(diǎn)是橢圓的一個(gè)焦點(diǎn)，則p=(）A．2B．3C．4D．83．（2021北京）已知拋物線(xiàn)SKIPIF1<0，SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0在曲線(xiàn)SKIPIF1<0上，且SKIPIF1<0，則SKIPIF1<0的橫坐標(biāo)是________；作SKIPIF1<0SKIPIF1<0軸于SKIPIF1<0，SKIPIF1<0=________．4．（2021新高考1卷）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，拋物線(xiàn)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(xiàn)方程為. 題組二：拋物線(xiàn)的簡(jiǎn)單幾何性質(zhì)及其應(yīng)用5．【2020全國(guó)Ⅰ卷】已知SKIPIF1<0為拋物線(xiàn)SKIPIF1<0上一點(diǎn)，點(diǎn)SKIPIF1<0到SKIPIF1<0的焦點(diǎn)的距離為SKIPIF1<0，到SKIPIF1<0軸的距離為SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2020北京卷）設(shè)拋物線(xiàn)的頂點(diǎn)為SKIPIF1<0，焦點(diǎn)為SKIPIF1<0，準(zhǔn)線(xiàn)為SKIPIF1<0．SKIPIF1<0是拋物線(xiàn)上異于SKIPIF1<0的一點(diǎn)，過(guò)SKIPIF1<0作SKIPIF1<0于SKIPIF1<0，則線(xiàn)段SKIPIF1<0的垂直平分線(xiàn)（）A．經(jīng)過(guò)點(diǎn)SKIPIF1<0 B．經(jīng)過(guò)點(diǎn)SKIPIF1<0C．平行于直線(xiàn)SKIPIF1<0 D．垂直于直線(xiàn)SKIPIF1<07.(2018全國(guó)1卷)設(shè)拋物線(xiàn)SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線(xiàn)與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0=()A．5 B．6 C．7 D．88.（2017新課標(biāo)Ⅱ）已知F是拋物線(xiàn)SKIPIF1<0：SKIPIF1<0的焦點(diǎn)，M是SKIPIF1<0上一點(diǎn)，F(xiàn)M的延長(zhǎng)線(xiàn)交SKIPIF1<0軸于點(diǎn)N．若M為FN的中點(diǎn)，則SKIPIF1<0．題組三：焦點(diǎn)弦問(wèn)題9.（2018全國(guó)2卷）設(shè)拋物線(xiàn)C:y2=4x的焦點(diǎn)為F，過(guò)F且斜率為k(k>0)的直線(xiàn)l與C交于A(yíng)，B兩點(diǎn)，|AB|=8．則SKIPIF1<0的方程是______________.10.（2019全國(guó)1卷）已知拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，斜率為SKIPIF1<0的直線(xiàn)SKIPIF1<0與SKIPIF1<0的交點(diǎn)為SKIPIF1<0，SKIPIF1<0，與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0,SKIPIF1<0，則SKIPIF1<0的方程是_______________.11．（2018全國(guó)3卷）已知點(diǎn)M(-1,1)和拋物線(xiàn)C:y2=4x，過(guò)C的焦點(diǎn)且斜率為k的直線(xiàn)與C交于A(yíng),B兩點(diǎn)．若∠AMB=900，則k=________．更多免費(fèi)資源，關(guān)注公眾號(hào)拾穗者的雜貨鋪12.（2014全國(guó)2卷）設(shè)F為拋物線(xiàn)C:SKIPIF1<0的焦點(diǎn)，過(guò)F且傾斜角為30°的直線(xiàn)交C于A(yíng),B兩點(diǎn)，O為坐標(biāo)原點(diǎn)，則SKIPIF1<0的面積為_(kāi)_____.題組四：拋物線(xiàn)中的最值問(wèn)題13.（2017全國(guó)1卷）已知SKIPIF1<0為拋物線(xiàn)SKIPIF1<0的焦點(diǎn)，過(guò)SKIPIF1<0作兩條互相垂直的直線(xiàn)SKIPIF1<0，直線(xiàn)SKIPIF1<0與SKIPIF1<0交于A(yíng)、B兩點(diǎn)，直線(xiàn)SKIPIF1<0與SKIPIF1<0交于D、E兩點(diǎn)，則|AB|+|DE|的最小值為（）A．16B．14C．12D．1014.（2021全國(guó)乙卷理）已知拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，且SKIPIF1<0與圓SKIPIF1<0上的點(diǎn)的最短距離為4.（1）求SKIPIF1<0；（2）若點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0為SKIPIF1<0的切線(xiàn)，切點(diǎn)為SKIPIF1<0，求SKIPIF1<0面積的最大值.15.（2021全國(guó)乙卷文）已知拋物線(xiàn)SKIPIF1<0:SKIPIF1<0的焦點(diǎn)SKIPIF1<0到準(zhǔn)線(xiàn)的距離為2.（1）求SKIPIF1<0的方程；（2）已知SKIPIF1<0為坐標(biāo)原點(diǎn)，點(diǎn)SKIPIF1<0在SKIPIF1<0上，點(diǎn)SKIPIF1<0滿(mǎn)足SKIPIF1<0，求直線(xiàn)SKIPIF1<0斜率的最大值．1.設(shè)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)M在C上，｜MF｜＝5，若以MF為直徑的圓過(guò)點(diǎn)（0,2），則C的方程為（）A.SKIPIF1<0或SKIPIF1<0B.SKIPIF1<0或SKIPIF1<0C.SKIPIF1<0或SKIPIF1<0D.SKIPIF1<0或SKIPIF1<02.以?huà)佄锞€(xiàn)C的頂點(diǎn)為圓心的圓交C于A(yíng)、B兩點(diǎn)，交C的準(zhǔn)線(xiàn)于D、E兩點(diǎn).已知|AB|=SKIPIF1<0，|DE|=SKIPIF1<0，則C的焦點(diǎn)到準(zhǔn)線(xiàn)的距離為（）.A．2B．4C．6D．83.已知直線(xiàn)SKIPIF1<0過(guò)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)，且與SKIPIF1<0的對(duì)稱(chēng)軸垂直，SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的準(zhǔn)線(xiàn)上一點(diǎn)，則SKIPIF1<0的面積為（）A．18B．24C．36D．484．過(guò)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)SKIPIF1<0，且斜率為SKIPIF1<0的直線(xiàn)交SKIPIF1<0于點(diǎn)SKIPIF1<0（SKIPIF1<0在SKIPIF1<0的軸上方），SKIPIF1<0為SKIPIF1<0的準(zhǔn)線(xiàn)，點(diǎn)SKIPIF1<0在SKIPIF1<0上且SKIPIF1<0，則SKIPIF1<0到直線(xiàn)SKIPIF1<0的距離為A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<05．已知SKIPIF1<0，拋物線(xiàn)SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0與拋物線(xiàn)SKIPIF1<0在第一象限的交點(diǎn)為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（）．A．1B．2C．3D．46.已知拋物線(xiàn)SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線(xiàn)為SKIPIF1<0，SKIPIF1<0是SKIPIF1<0上一點(diǎn)，SKIPIF1<0是直線(xiàn)SKIPIF1<0與SKIPIF1<0的一個(gè)交點(diǎn)，若SKIPIF1<0，則SKIPIF1<0=_______.7.設(shè)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線(xiàn)為SKIPIF1<0，SKIPIF1<0，已知以SKIPIF1<0為圓心