第07講拋物線(精練）A夯實(shí)基礎(chǔ)B能力提升C綜合素養(yǎng)A夯實(shí)基礎(chǔ)一、單選題1．拋物線SKIPIF1<0的焦點(diǎn)坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若拋物線SKIPIF1<0上的點(diǎn)P的橫坐標(biāo)為3，則點(diǎn)P到焦點(diǎn)的距離是（

）．A．7 B．6 C．5 D．43．直線SKIPIF1<0過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，且與SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，則SKIPIF1<0（

）A．6 B．8 C．2 D．44．已知拋物線SKIPIF1<0的焦點(diǎn)F、M是拋物線SKIPIF1<0上位于第一象限內(nèi)的一點(diǎn)，O為坐標(biāo)原點(diǎn)，若SKIPIF1<0的外接圓D與拋物線SKIPIF1<0的準(zhǔn)線相切，則圓D與直線SKIPIF1<0相交得到的弦長為（

）A．SKIPIF1<0 B．4 C．SKIPIF1<0 D．SKIPIF1<05．已知點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0的焦點(diǎn)，點(diǎn)M為拋物線上的任意一點(diǎn)，SKIPIF1<0為平面上定點(diǎn)，則SKIPIF1<0的最小值為（

）A．3 B．4 C．5 D．66．已知拋物線SKIPIF1<0：SKIPIF1<0焦點(diǎn)為SKIPIF1<0，SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，且點(diǎn)SKIPIF1<0到拋物線的準(zhǔn)線的距離為3，點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上運(yùn)動(dòng)，則點(diǎn)SKIPIF1<0到直線SKIPIF1<0：SKIPIF1<0的最小距離是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<07．已知點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，SKIPIF1<0是拋物線的焦點(diǎn)，SKIPIF1<0是圓SKIPIF1<0的圓心，則SKIPIF1<0的最小值為（

）A．7 B．6 C．5 D．48．已知過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0且傾斜角為SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)（SKIPIF1<0在SKIPIF1<0的右邊），SKIPIF1<0為SKIPIF1<0上一點(diǎn)，SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．5二、多選題9．在平面直角坐標(biāo)系SKIPIF1<0中，拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，SKIPIF1<0為拋物線上一點(diǎn)，SKIPIF1<0，SKIPIF1<0為垂足.若直線SKIPIF1<0的斜率SKIPIF1<0，則下列結(jié)論正確的是（

）A．準(zhǔn)線方程為SKIPIF1<0 B．焦點(diǎn)坐標(biāo)SKIPIF1<0C．點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0 D．SKIPIF1<0的長為310．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0都在拋物線上，且SKIPIF1<0，則下列結(jié)論正確的是（

）A．拋物線方程為SKIPIF1<0B．SKIPIF1<0是SKIPIF1<0的重心C．SKIPIF1<0D．SKIPIF1<0三、填空題11．位于德國東部薩克森州的萊科勃克橋（如圖所示）有“仙境之橋”之稱，它的橋形可近似地看成拋物線的一部分．該橋的高度為SKIPIF1<0米，跨徑為SKIPIF1<0米，則橋形對應(yīng)的拋物線的焦點(diǎn)到準(zhǔn)線的距離為________米．（結(jié)果用SKIPIF1<0，SKIPIF1<0表示）12．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______．四、解答題13．若SKIPIF1<0，SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，SKIPIF1<0為拋物線上任意一點(diǎn)，求SKIPIF1<0的最小值及取得最小值時(shí)的SKIPIF1<0的坐標(biāo)．14．圖中是拋物線形拱橋，當(dāng)水面在l時(shí)，拱頂離水面2m，水面寬4m．水面下降1m后，水面寬多少？（精確到0.1m，參考數(shù)據(jù)SKIPIF1<0）．B能力提升1．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上，直線SKIPIF1<0交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，若SKIPIF1<0，則點(diǎn)SKIPIF1<0到準(zhǔn)線SKIPIF1<0的距離為（

）A．6 B．5 C．4 D．32．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0上一點(diǎn)，點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．33．已知點(diǎn)M（0，4），點(diǎn)P在曲線SKIPIF1<0上運(yùn)動(dòng)，點(diǎn)Q在圓SKIPIF1<0上運(yùn)動(dòng)，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．6C綜合素養(yǎng)1．已知拋物線SKIPIF1<0，SKIPIF1<0是拋物線上一點(diǎn)，設(shè)點(diǎn)SKIPIF1<0（SKIPIF1<0），求|SKIPIF1<0|的最小值，并指出此時(shí)點(diǎn)SKIPIF1<0的坐標(biāo).2．已知橢圓C1：SKIPIF1<0(a>b>0)的左、右焦點(diǎn)分別為F1、F2，其中F2也是拋物線C2：y2＝4x的焦點(diǎn)，M是C1與C2在第一象限的交點(diǎn)，且|MF2|＝SKIPIF1<0.(1)求橢圓C1的方程；(2)點(diǎn)