新高考數(shù)學(xué)一輪復(fù)習(xí) 圓錐曲線專項(xiàng)重難點(diǎn)突破專題18 拋物線中的參數(shù)及范圍問(wèn)題(原卷版)

專題18拋物線中的參數(shù)及范圍問(wèn)題限時(shí)：120分鐘滿分：150分一、單選題：本大題共8小題，每個(gè)小題5分，共40分.在每小題給出的選項(xiàng)中，只有一項(xiàng)是符合題目要求的.1．已知SKIPIF1<0為拋物線SKIPIF1<0上一點(diǎn)，SKIPIF1<0為焦點(diǎn)，過(guò)SKIPIF1<0作SKIPIF1<0的準(zhǔn)線的垂線，垂足為SKIPIF1<0，若SKIPIF1<0的周長(zhǎng)不小于30，則點(diǎn)SKIPIF1<0的縱坐標(biāo)的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，過(guò)SKIPIF1<0的直線SKIPIF1<0與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若在SKIPIF1<0軸負(fù)半軸上存在一點(diǎn)SKIPIF1<0，使得SKIPIF1<0為銳角，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．若拋物線SKIPIF1<0上存在不同的兩點(diǎn)關(guān)于直線SKIPIF1<0對(duì)稱，則實(shí)數(shù)p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)SKIPIF1<0與雙曲線SKIPIF1<0的右焦點(diǎn)重合，斜率為SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0的兩個(gè)交點(diǎn)為SKIPIF1<0，SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．在平面直角坐標(biāo)系SKIPIF1<0中，若拋物線SKIPIF1<0的準(zhǔn)線與圓SKIPIF1<0相切于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與拋物線SKIPIF1<0切于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0的直線SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，分別在點(diǎn)SKIPIF1<0處作SKIPIF1<0的兩條切線，兩條切線交于點(diǎn)SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，且拋物線上存在不同的兩點(diǎn)SKIPIF1<0，SKIPIF1<0，使得直線SKIPIF1<0，SKIPIF1<0的斜率SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，若線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則直線SKIPIF1<0的斜率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已如拋物線SKIPIF1<0的焦點(diǎn)是SKIPIF1<0，點(diǎn)SKIPIF1<0是其準(zhǔn)線上一個(gè)動(dòng)點(diǎn)，其中SKIPIF1<0．過(guò)點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于A，SKIPIF1<0兩點(diǎn)，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．若SKIPIF1<0，則直線SKIPIF1<0的斜率SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題：本大題共4小題，每個(gè)小題5分，共20分.在每小題給出的選項(xiàng)中，只有一項(xiàng)或者多項(xiàng)是符合題目要求的.9．已知點(diǎn)SKIPIF1<0，拋物線SKIPIF1<0的焦點(diǎn)為F，過(guò)F的直線l交C于P，Q兩點(diǎn)，則（

）A．SKIPIF1<0的最大值為SKIPIF1<0B．SKIPIF1<0的面積最小值為2C．當(dāng)SKIPIF1<0取到最大值時(shí)，直線AP與C相切D．當(dāng)SKIPIF1<0取到最大值時(shí)，SKIPIF1<010．已知SKIPIF1<0是拋物線SKIPIF1<0SKIPIF1<0內(nèi)一動(dòng)點(diǎn)，直線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0且與拋物線SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，則下列說(shuō)法正確的是（

）A．SKIPIF1<0時(shí)，SKIPIF1<0的最小值為SKIPIF1<0B．SKIPIF1<0的取值范圍是SKIPIF1<0C．當(dāng)點(diǎn)SKIPIF1<0是弦SKIPIF1<0的中點(diǎn)時(shí)，直線SKIPIF1<0的斜率為SKIPIF1<0D．當(dāng)點(diǎn)SKIPIF1<0是弦SKIPIF1<0的中點(diǎn)時(shí)，SKIPIF1<0軸上存在一定點(diǎn)SKIPIF1<0，都有SKIPIF1<011．已知拋物線C：SKIPIF1<0的焦點(diǎn)為F，P，Q為C上兩點(diǎn)，則下列說(shuō)法正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0的最小值為4B．若SKIPIF1<0，記SKIPIF1<0，則SKIPIF1<0C．過(guò)點(diǎn)SKIPIF1<0與C只有一個(gè)公共點(diǎn)的直線有且僅有兩條D．以PQ為直徑的圓與C的準(zhǔn)線相切，則直線PQ過(guò)F12．設(shè)SKIPIF1<0是拋物線SKIPIF1<0：SKIPIF1<0上的兩點(diǎn)，SKIPIF1<0是坐標(biāo)原點(diǎn)，下列結(jié)論成立的是（

）A．若直線SKIPIF1<0過(guò)拋物線的焦點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為1B．有且只有兩條直線過(guò)點(diǎn)SKIPIF1<0且與拋物線SKIPIF1<0只有一個(gè)公共點(diǎn)C．若SKIPIF1<0，則SKIPIF1<0為定值D．若SKIPIF1<0，則SKIPIF1<0三、填空題：本大題共4小題，每小題5分，共20分.把答案填在答題卡中的橫線上.13．已知SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，SKIPIF1<0是拋物線的焦點(diǎn)，若點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是．14．已知斜率為SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0軸上方不同的兩點(diǎn)SKIPIF1<0、SKIPIF1<0，記直線SKIPIF1<0、SKIPIF1<0的斜率分別為SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0的取值范圍是.15．已知拋物線SKIPIF1<0方程為SKIPIF1<0，SKIPIF1<0為其焦點(diǎn)，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，且拋物線在SKIPIF1<0、SKIPIF1<0兩點(diǎn)處的切線分別交SKIPIF1<0軸于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的取值范圍為．16．如圖，已知拋物線SKIPIF1<0，點(diǎn)SKIPIF1<0為拋物線上一動(dòng)點(diǎn)，以C為圓心的圓過(guò)定點(diǎn)SKIPIF1<0，且SKIPIF1<0與x軸交于M，N兩點(diǎn)（M點(diǎn)在N點(diǎn)的左側(cè)），則SKIPIF1<0的取值范圍是．四、解答題：本大題共6小題，共70分.解答應(yīng)寫(xiě)出必要的文字說(shuō)明、證明過(guò)程或演算步驟．17．已知拋物線SKIPIF1<0的頂點(diǎn)在原點(diǎn)，焦點(diǎn)在直線SKIPIF1<0上．(1)求拋物線SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)過(guò)點(diǎn)SKIPIF1<0的直線m與焦點(diǎn)在x軸上的拋物線SKIPIF1<0交于A，B兩點(diǎn)，若原點(diǎn)O在以線段AB為直徑的圓外，求實(shí)數(shù)a的取值范圍．18．已知拋物線SKIPIF1<0焦點(diǎn)為F，點(diǎn)SKIPIF1<0在拋物線上，SKIPIF1<0.(1)求拋物線方程；(2)過(guò)焦點(diǎn)F直線l與拋物線交于MN兩點(diǎn)，若MN最小值為4，且SKIPIF1<0是鈍角，求直線斜率范圍.19．設(shè)點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0上，SKIPIF1<0的焦點(diǎn)為SKIPIF1<0．SKIPIF1<0、SKIPIF1<0為過(guò)SKIPIF1<0的兩條傾斜角互補(bǔ)的直線，且SKIPIF1<0、SKIPIF1<0與SKIPIF1<0的另一交點(diǎn)分別為SKIPIF1<0、SKIPIF1<0．已知直線SKIPIF1<0的斜率為SKIPIF1<0．(1)求直線SKIPIF1<0的斜率；(2)記SKIPIF1<0、SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)分別為SKIPIF1<0、SKIPIF1<0．設(shè)SKIPIF1<0和SKIPIF1<0分別為SKIPIF1<0和SKIPIF1<0的面積，當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的取值范圍．20．已知點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0SKIPIF1<0之間的距離為2，拋物線SKIPIF1<0經(jīng)過(guò)點(diǎn)N，過(guò)點(diǎn)M的直線l與拋物線C有兩個(gè)不同的交點(diǎn)A，B，點(diǎn)E，F(xiàn)分別在直線SKIPIF1<0，SKIPIF1<0上，且SKIPIF1<0