新高考數(shù)學(xué)一輪復(fù)習(xí)百題刷過關(guān)專題26 圓錐曲線巧設(shè)直線必刷100題(原卷版)

專題26圓錐曲線巧設(shè)直線必刷100題方法提示:在圓錐曲線聯(lián)立與設(shè)線的問題當(dāng)中,設(shè)直線的方法比較多.常見有幾下幾種類型:①SKIPIF1<0當(dāng)題干中直接或者隱含直線過定點(diǎn)SKIPIF1<0時(shí),可設(shè)點(diǎn)斜式SKIPIF1<0局限性:局限性:不能表示垂直于SKIPIF1<0軸的直線,需要單獨(dú)討論.②SKIPIF1<0當(dāng)題干中含有過SKIPIF1<0軸上一定點(diǎn)SKIPIF1<0時(shí),或者在解題步驟中需要SKIPIF1<0或SKIPIF1<0,需要消掉SKIPIF1<0,保留SKIPIF1<0時(shí),設(shè)SKIPIF1<0會簡化解題步驟和計(jì)算量.局限性:不能表示垂直于SKIPIF1<0軸的直線,需要單獨(dú)討論.③SKIPIF1<0,當(dāng)題干中含有過SKIPIF1<0軸上一定點(diǎn)SKIPIF1<0時(shí),或者在解題步驟中需要SKIPIF1<0或SKIPIF1<0,需要消掉SKIPIF1<0,保留SKIPIF1<0時(shí),設(shè)SKIPIF1<0會簡化解題步驟和計(jì)算量.局限性:不能表示平行于SKIPIF1<0軸的直線,需要單獨(dú)討論.一、單選題1．已知直線SKIPIF1<0與拋物線SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)為SKIPIF1<0，且拋物線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），則SKIPIF1<0的值為（）A．4 B．2 C．1 D．SKIPIF1<02．已知弦SKIPIF1<0經(jīng)過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，設(shè)SKIPIF1<0，SKIPIF1<0，則下列說法中錯(cuò)誤的是（）A．當(dāng)SKIPIF1<0與SKIPIF1<0軸垂直時(shí)，SKIPIF1<0最小B．SKIPIF1<0C．以弦SKIPIF1<0為直徑的圓與直線SKIPIF1<0相離D．SKIPIF1<03．過點(diǎn)SKIPIF1<0的直線與拋物線SKIPIF1<0交于A，B兩點(diǎn)，若線段AB中點(diǎn)的橫坐標(biāo)為2，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若直線y＝kx+2與雙曲線x2﹣y2＝6的右支交于不同的兩點(diǎn)，則k的取值范圍是（）A．SKIPIF1<0，SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知過拋物線C：y2＝4x的焦點(diǎn)F且傾斜角為30°的直線交C于A，B兩點(diǎn)，Q為AB的中點(diǎn)，P為C上一點(diǎn)，則|PF|+|PQ|的最小值為（）A．5 B．6 C．7 D．86．已知拋物線y2＝4x，直線l與拋物線交于A、B兩點(diǎn)，若線段AB中點(diǎn)的縱坐標(biāo)為2，則直線AB的斜率為（）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．17．已知直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)（點(diǎn)SKIPIF1<0在第一象限，點(diǎn)SKIPIF1<0在第四象限），與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，若線段SKIPIF1<0的中點(diǎn)的橫坐標(biāo)為3，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．平面直角坐標(biāo)系SKIPIF1<0中，已知直線l與拋物線SKIPIF1<0交于A、B兩點(diǎn)，SKIPIF1<0、SKIPIF1<0的斜率分別為SKIPIF1<0和SKIPIF1<0，滿足SKIPIF1<0，F(xiàn)是拋物線的焦點(diǎn)，則SKIPIF1<0的面積的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知拋物線SKIPIF1<0，SKIPIF1<0和SKIPIF1<0分別為拋物線上的兩個(gè)動點(diǎn)，若SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），弦SKIPIF1<0恒過定點(diǎn)SKIPIF1<0，則拋物線方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．已知點(diǎn)F為拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)F的直線l交拋物線C于A，B兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0（）A．9 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知拋物線SKIPIF1<0的焦點(diǎn)為F，經(jīng)過點(diǎn)F的直線與拋物線C交于A?B兩點(diǎn)，若AB的中點(diǎn)為SKIPIF1<0，則線段AB的長為（）A．SKIPIF1<0 B．4 C．5 D．4或512．已知點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)SKIPIF1<0的直SKIPIF1<0線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．已知過SKIPIF1<0的直線與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0為弦SKIPIF1<0的中點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0與拋物線的另一個(gè)交點(diǎn)為SKIPIF1<0，則兩點(diǎn)SKIPIF1<0、SKIPIF1<0縱坐標(biāo)的比值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．橢圓SKIPIF1<0上到直線SKIPIF1<0距離最近的點(diǎn)的坐標(biāo)是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<015．過拋物線SKIPIF1<0：SKIPIF1<0焦點(diǎn)F的直線與拋物線相交于A，B兩點(diǎn)，SKIPIF1<0，O為坐標(biāo)原點(diǎn)，且△SKIPIF1<0的面積為SKIPIF1<0，則拋物線C的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．已知拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0到其準(zhǔn)線的距離為2，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．917．設(shè)F為橢圓SKIPIF1<0的右焦點(diǎn)，過點(diǎn)SKIPIF1<0的直線與橢圓C交于SKIPIF1<0兩點(diǎn)，設(shè)直線SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0為（）A．1 B．-1 C．4 D．-418．設(shè)拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，且SKIPIF1<0．設(shè)直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）．則直線SKIPIF1<0過定點(diǎn)（）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．過橢圓SKIPIF1<0的焦點(diǎn)SKIPIF1<0的弦中最短弦長是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．已知F是橢圓SKIPIF1<0的一個(gè)焦點(diǎn)，AB為過橢圓中心的一條弦，則△ABF面積的最大值為（）A．6 B．15 C．20 D．1221．過雙曲線SKIPIF1<0的右焦點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線交雙曲線右支于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則雙曲線的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<022．若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0有且只有一個(gè)公共點(diǎn)，則這樣的直線SKIPIF1<0的共有（）A．一條 B．兩條 C．三條 D．四條23．如圖，在拋物線SKIPIF1<0的準(zhǔn)線上任取一點(diǎn)SKIPIF1<0（異于準(zhǔn)線與x軸的交點(diǎn)），連接SKIPIF1<0并延長交拋物線于點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0作平行于SKIPIF1<0軸的直線交拋物線于點(diǎn)SKIPIF1<0，則直線SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)坐標(biāo)為（）A．與點(diǎn)SKIPIF1<0位置有關(guān)B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<024．已知拋物線C：y2＝8ax(a＞0)的焦點(diǎn)F與雙曲線D：SKIPIF1<0的一個(gè)焦點(diǎn)重合，過點(diǎn)F的直線與拋物線C交于點(diǎn)A，B，則|AF|＋2|BF|的最小值為（）A．3＋4SKIPIF1<0 B．6+4SKIPIF1<0 C．7 D．1025．已知SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0、SKIPIF1<0分別是橢圓SKIPIF1<0的左、右頂點(diǎn)，SKIPIF1<0是橢圓SKIPIF1<0上不同于SKIPIF1<0、SKIPIF1<0的動點(diǎn)，直線SKIPIF1<0、SKIPIF1<0分別與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0、SKIPIF1<0.則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．已知點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0的焦點(diǎn)，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<027．已知橢圓SKIPIF1<0：SKIPIF1<0上有一動點(diǎn)SKIPIF1<0（異于頂點(diǎn)），點(diǎn)SKIPIF1<0?SKIPIF1<0分別在SKIPIF1<0?SKIPIF1<0軸上，使得SKIPIF1<0為SKIPIF1<0的中點(diǎn)，若SKIPIF1<0軸上一點(diǎn)SKIPIF1<0，滿足SKIPIF1<0，則SKIPIF1<0的最小值為（）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．528．已知橢圓SKIPIF1<0，P為E的長軸上任意一點(diǎn)，過點(diǎn)P作斜率為SKIPIF1<0的直線l與E交于M，N兩點(diǎn)，則SKIPIF1<0的值為（）A．4 B．5 C．6 D．729．已知直線SKIPIF1<0過拋物線SKIPIF1<0（SKIPIF1<0）的焦點(diǎn)SKIPIF1<0，與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).若直線SKIPIF1<0的斜率為SKIPIF1<0，SKIPIF1<0，以SKIPIF1<0為直徑的圓與SKIPIF1<0軸交于SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<030．已知拋物線SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0，過SKIPIF1<0點(diǎn)作直線SKIPIF1<0與上述兩曲線自左而右依次交于點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．2 C．3 D．SKIPIF1<031．已知斜率為SKIPIF1<0的直線SKIPIF1<0經(jīng)過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0，并與拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0的值為（）A．1 B．2 C．3 D．432．兩個(gè)長軸在SKIPIF1<0軸上、中心在坐標(biāo)原點(diǎn)且離心率相同的橢圓．若SKIPIF1<0，SKIPIF1<0分別為外層橢圓的左頂點(diǎn)和上頂點(diǎn)，分別向內(nèi)層橢圓作切線SKIPIF1<0，SKIPIF1<0，切點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且兩切線斜率之積等于SKIPIF1<0，則橢圓的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<033．過點(diǎn)（1，2）且與雙曲線SKIPIF1<0沒有交點(diǎn)的直線l斜率的取值范圍是（）A．（2，+∞） B．[2，+∞） C．[﹣2，2] D．[﹣2，+∞）34．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的中點(diǎn)SKIPIF1<0到SKIPIF1<0的準(zhǔn)線SKIPIF1<0的距離的最小值為（）A．2 B．4 C．5 D．635．已知F是拋物線C：SKIPIF1<0的焦點(diǎn)，O為坐標(biāo)原點(diǎn)，過F的直線交C于A，B兩點(diǎn)，則三角形OAB面積的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．236．已知拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交拋物線于A，B兩點(diǎn)，F(xiàn)為拋物線的焦點(diǎn)，若SKIPIF1<0，O為坐標(biāo)原點(diǎn)，則四邊形SKIPIF1<0的面積是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<037．對正整數(shù)SKIPIF1<0，設(shè)拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0任作直線SKIPIF1<0交拋物線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和公式是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<038．已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0：SKIPIF1<0的兩個(gè)焦點(diǎn)，左頂點(diǎn)為A，過點(diǎn)SKIPIF1<0的直線交橢圓SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<039．設(shè)A，B分別是雙曲線x2-SKIPIF1<0=1的左、右頂點(diǎn)，設(shè)過PSKIPIF1<0的直線PA，PB與雙曲線分別交于點(diǎn)M，N，直線MN交x軸于點(diǎn)Q，過Q的直線交雙曲線的右支于S，T兩點(diǎn)，且SKIPIF1<0=2SKIPIF1<0，則△BST的面積為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<040．已知斜率不為0的直線SKIPIF1<0過橢圓SKIPIF1<0的左焦點(diǎn)SKIPIF1<0且交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0軸上的點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0第II卷（非選擇題）二、填空題41．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線在第一象限內(nèi)交于點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn).若SKIPIF1<0，則SKIPIF1<0的面積為___________.42．已知直線l分別切拋物線SKIPIF1<0（SKIPIF1<0）和圓SKIPIF1<0于點(diǎn)A，B（A，B不重合），點(diǎn)F為拋物線的焦點(diǎn)，當(dāng)SKIPIF1<0取得最小值時(shí)，SKIPIF1<0___________.43．拋物線C：y2=4SKIPIF1<0，直線SKIPIF1<0繞SKIPIF1<0旋轉(zhuǎn)，若直線SKIPIF1<0與拋物線C有兩個(gè)交點(diǎn)．則直線SKIPIF1<0的斜率k的取值范圍是_________________44．已知點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）上，左頂點(diǎn)為SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0分別為橢圓SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0的最大值和最小值分別為4和SKIPIF1<0．直線SKIPIF1<0點(diǎn)SKIPIF1<0，且與SKIPIF1<0平行，過SKIPIF1<0，SKIPIF1<0兩點(diǎn)作SKIPIF1<0的垂線，垂足分別為SKIPIF1<0，SKIPIF1<0，當(dāng)矩形SKIPIF1<0的面積為SKIPIF1<0時(shí)，則直線SKIPIF1<0的斜率是______．45．已知斜率為1的直線l經(jīng)過橢圓SKIPIF1<0的一個(gè)焦點(diǎn)，與橢圓交于A，B兩點(diǎn).直線l1，l2分別過點(diǎn)A，B，且與x軸平行，在直線l1，l2上分別取點(diǎn)M，N（M，N分別在點(diǎn)A，B的右側(cè)），分別作∠ABN和∠BAM的角平分線相交于點(diǎn)P，則SKIPIF1<0PAB的面積為___________.46．已知拋物線C：y2＝4x的焦點(diǎn)為F，M為C上的動點(diǎn)，直線MF與C的另一交點(diǎn)為A，M關(guān)于點(diǎn)P（12，4）的對稱點(diǎn)為B，當(dāng)|MA|+|AB|的值最小時(shí)，直線AM的方程為__．47．已知點(diǎn)SKIPIF1<0在拋物線SKIPIF1<0：SKIPIF1<0上，過點(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的傾斜角為________．48．點(diǎn)SKIPIF1<0?SKIPIF1<0分別為橢圓SKIPIF1<0的左?右頂點(diǎn)，直線SKIPIF1<0與橢圓相交于SKIPIF1<0?SKIPIF1<0兩點(diǎn)，記直線SKIPIF1<0?SKIPIF1<0的斜率分別為SKIPIF1<0?SKIPIF1<0，則SKIPIF1<0的最小值為___________49．已知橢圓SKIPIF1<0，一組平行直線的斜率為SKIPIF1<0，經(jīng)計(jì)算當(dāng)這些平行線與橢圓相交時(shí)，被橢圓截得的線段的中點(diǎn)在定直線l上，則直線l的方程為___________.50．已知直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).且線段SKIPIF1<0的中點(diǎn)在直線SKIPIF1<0上，若SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），則SKIPIF1<0的面積為_______________________．51．已知直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn).且線段SKIPIF1<0的中點(diǎn)在直線SKIPIF1<0上，若SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），則SKIPIF1<0的面積為______．52．已知拋物線C：y2＝4x，過焦點(diǎn)F的直線l與拋物線C交于A，B兩點(diǎn)，若線段AF，BF的中點(diǎn)在y軸上的射影分別為P，Q，且｜PQ｜＝4，則直線l的方程為__________．53．已知拋物線C：SKIPIF1<0的焦點(diǎn)為F，過點(diǎn)F斜率為k的直線l與C交于M，N兩點(diǎn)，若O為坐標(biāo)原點(diǎn)，SKIPIF1<0OMN的重心為點(diǎn)GSKIPIF1<0，則k=__________.54．如圖，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0、SKIPIF1<0與拋物線SKIPIF1<0相交，其中SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0過E的焦點(diǎn)F，若SKIPIF1<0、SKIPIF1<0的斜率為SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為_______．55．已知點(diǎn)P為直線l：x＝－2上任意一點(diǎn)，過點(diǎn)P作拋物線y2＝2px(p＞0)的兩條切線，切點(diǎn)分別為A(x1，y1)，B(x2，y2)，若x1x2為定值，則該定值為____．56．已知拋物線SKIPIF1<0：SKIPIF1<0，過焦點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0的準(zhǔn)線上的投影分別為SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0__________.57．已知橢圓SKIPIF1<0，過橢圓在第二象限上的任意一點(diǎn)SKIPIF1<0作橢圓的切線與SKIPIF1<0軸相交于SKIPIF1<0點(diǎn)，SKIPIF1<0是坐標(biāo)原點(diǎn)，過點(diǎn)SKIPIF1<0作SKIPIF1<0，垂足為SKIPIF1<0，則SKIPIF1<0的取值范圍是______________58．已知橢圓C：SKIPIF1<0＝1，直線l過橢圓C的左焦點(diǎn)F且交橢圓于A，B兩點(diǎn)，AB的中垂線交x軸于M點(diǎn)，則SKIPIF1<0的取值范圍為__．59．拋物線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SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0的準(zhǔn)線與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0，若SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0___________.60．已知斜率不為0的直線SKIPIF1<0過橢圓SKIPIF1<0：SKIPIF1<0的左焦點(diǎn)SKIPIF1<0且交橢圓于SKIPIF1<0兩點(diǎn)，SKIPIF1<0軸上的點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是___________.三、解答題61．己知拋物線C：y2=2px(p>0)，過拋物線的焦點(diǎn)F且垂直于x軸的直線交拋物線于不同的兩點(diǎn)A，B,且SKIPIF1<0（1）求拋物線C的方程；（2）若不經(jīng)過坐標(biāo)原點(diǎn)O的直線SKIPIF1<0與拋物線C相交于不同的兩點(diǎn)M，N,且滿足SKIPIF1<0.證明直線SKIPIF1<0過x軸上一定點(diǎn)Q，并求出點(diǎn)Q的坐標(biāo).62．設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過焦點(diǎn)SKIPIF1<0作直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn).（1）若SKIPIF1<0，求直線SKIPIF1<0的方程；（2）若點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0分別與拋物線SKIPIF1<0的準(zhǔn)線相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求證：SKIPIF1<0.63．設(shè)拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過焦點(diǎn)SKIPIF1<0作直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．（1）若SKIPIF1<0，求直線SKIPIF1<0的方程；（2）設(shè)SKIPIF1<0為拋物線SKIPIF1<0上異于SKIPIF1<0，SKIPIF1<0的任意一點(diǎn)，直線SKIPIF1<0，SKIPIF1<0分別與拋物線SKIPIF1<0的準(zhǔn)線相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求證：以線段SKIPIF1<0為直徑的圓經(jīng)過SKIPIF1<0軸上的定點(diǎn)．64．在平面直角坐標(biāo)系SKIPIF1<0中，點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0，點(diǎn)P是平面內(nèi)一動點(diǎn)，且直線SKIPIF1<0的斜率與直線SKIPIF1<0的斜率之積為SKIPIF1<0，記點(diǎn)P的軌跡為曲線C．（1）求C的方程，并說明C是什么曲線；（2）過點(diǎn)SKIPIF1<0的直線l與C交于A，B兩點(diǎn)，則在x軸上是否存在定點(diǎn)D，使得SKIPIF1<0的值為定值？若存在，求出點(diǎn)D的坐標(biāo)和該定值；若不存在，請說明理由．65．已知拋物線SKIPIF1<0，點(diǎn)SKIPIF1<0是拋物線SKIPIF1<0上的點(diǎn)．（1）求拋物線的方程及SKIPIF1<0的值；（2）直線SKIPIF1<0與拋物線交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的最小值并證明直線SKIPIF1<0過定點(diǎn)．66．已知SKIPIF1<0是拋物線SKIPIF1<0（SKIPIF1<0）的焦點(diǎn)，過點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0.（1）求拋物線的標(biāo)準(zhǔn)方程；（2）動直線SKIPIF1<0垂直于線段SKIPIF1<0，且與拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，當(dāng)四邊形SKIPIF1<0面積為SKIPIF1<0時(shí)，求直線SKIPIF1<0的方程.67．橢圓的兩個(gè)焦點(diǎn)坐標(biāo)分別為F1(－SKIPIF1<0，0)和F2(SKIPIF1<0，0)，且橢圓過點(diǎn)SKIPIF1<0.（1）求橢圓方程；（2）過點(diǎn)SKIPIF1<0作不與y軸垂直的直線l交該橢圓于M，N兩點(diǎn)，A為橢圓的左頂點(diǎn)，試判斷∠MAN的大小是否為定值，并說明理由.68．已知橢圓SKIPIF1<0和拋物線SKIPIF1<0，點(diǎn)F為SKIPIF1<0的右焦點(diǎn)，點(diǎn)H為SKIPIF1<0的焦點(diǎn)．（1）過點(diǎn)F作SKIPIF1<0的切線，切點(diǎn)為P，SKIPIF1<0求拋物線SKIPIF1<0的方程；（2）過點(diǎn)H的直線l交SKIPIF1<0于P，Q兩點(diǎn)，點(diǎn)M滿足SKIPIF1<0，（O為坐標(biāo)原點(diǎn)），且點(diǎn)M在線段SKIPIF1<0上，記SKIPIF1<0的面積為SKIPIF1<0的面積為SKIPIF1<0，求SKIPIF1<0的取值范圍．69．已知橢圓SKIPIF1<0的方程為：SKIPIF1<0（SKIPIF1<0），離心率為SKIPIF1<0，橢圓上的動點(diǎn)SKIPIF1<0到右焦點(diǎn)SKIPIF1<0距離的最大值為SKIPIF1<0．（1）求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）過右焦點(diǎn)SKIPIF1<0作不平行于SKIPIF1<0軸的直線SKIPIF1<0交橢圓于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸對稱點(diǎn)為SKIPIF1<0，求證：直線SKIPIF1<0過定點(diǎn)．70．已知雙曲線SKIPIF1<0的兩個(gè)焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，動點(diǎn)SKIPIF1<0滿足SKIPIF1<0.（1）求動點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；（2）若軌跡SKIPIF1<0上存在兩點(diǎn)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0（SKIPIF1<0，SKIPIF1<0分別為直線SKIPIF1<0，SKIPIF1<0的斜率），求直線SKIPIF1<0的斜率的取值范圍.71．已知橢圓：SKIPIF1<0的離心率SKIPIF1<0，連接橢圓的四個(gè)頂點(diǎn)得到的菱形的面積為4.（1）求橢圓的標(biāo)準(zhǔn)方程；（2）設(shè)直線SKIPIF1<0與橢圓相交于不同的兩點(diǎn)SKIPIF1<0，已知點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0且SKIPIF1<0，求直線SKIPIF1<0的傾斜角.72．設(shè)SKIPIF1<0分別是平面直角坐標(biāo)系中SKIPIF1<0軸正方向上的單位向量，若向量SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，其中SKIPIF1<0.（1）求動點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0的方程；（2）過點(diǎn)SKIPIF1<0作直線SKIPIF1<0與軌跡SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，設(shè)SKIPIF1<0，是否存在直線SKIPIF1<0，使得四邊形SKIPIF1<0是矩形？若存在，求出直線SKIPIF1<0的方程；若不存在，試說明理由.73．已知拋物線SKIPIF1<0上的一點(diǎn)SKIPIF1<0到焦點(diǎn)SKIPIF1<0的距離等于3.（1）求拋物線SKIPIF1<0的方程；（2）若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0.求直線SKIPIF1<0的斜率.74．已知點(diǎn)SKIPIF1<0皆為曲線C上點(diǎn)，P為曲線C上異于A，B的任意一點(diǎn)，且滿足直線PA的斜率與直線PB的斜率之積為SKIPIF1<0.（1）求曲線C的方程；（2）若曲線SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過SKIPIF1<0的直線SKIPIF1<0與曲線SKIPIF1<0交于SKIPIF1<0，求證：直線SKIPIF1<0與直線SKIPIF1<0斜率之和為定值.75．已知橢圓C：SKIPIF1<0，SKIPIF1<0，且橢圓C右焦點(diǎn)為SKIPIF1<0，O為坐標(biāo)原點(diǎn).（1）求橢圓C的方程；（2）過SKIPIF1<0的直線l交橢圓C于A，B兩點(diǎn)，若SKIPIF1<0，求直線l的方程.76．已知點(diǎn)SKIPIF1<0皆為曲線C上點(diǎn)，P為曲線C上異于M，N的任意一點(diǎn)，且滿足直線PM的斜率與直線PN的斜率之積為SKIPIF1<0.（1）求曲線C的方程；（2）若曲線上點(diǎn)SKIPIF1<0，經(jīng)過曲線C右焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0與曲線C交于SKIPIF1<0，SKIPIF1<0（異于SKIPIF1<0）兩點(diǎn)，與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，求證：SKIPIF1<0.77．已知雙曲線SKIPIF1<0的離心率為2，且過點(diǎn)SKIPIF1<0.（1）求C的方程；（2）若斜率為SKIPIF1<0的直線l與C交于P，Q兩點(diǎn)，且與x軸交于點(diǎn)M，若Q為PM的中點(diǎn)，求l的方程.78．已知橢圓SKIPIF1<0的長軸長是SKIPIF1<0，以其短軸為直徑的圓過橢圓的焦點(diǎn)（1）求橢圓E的方程；（2）過橢圓E左焦點(diǎn)作不與坐標(biāo)軸垂直的直線，交橢圓于M，N兩點(diǎn)，線段SKIPIF1<0的垂直平分線與y軸負(fù)半軸交于點(diǎn)Q，若點(diǎn)Q的縱坐標(biāo)的最大值是SKIPIF1<0，求SKIPIF1<0的最小值；79．已知拋物線C：SKIPIF1<0的焦點(diǎn)到其準(zhǔn)線的距離為2，（1）求拋物線C的標(biāo)準(zhǔn)方程；（2）直線l過點(diǎn)SKIPIF1<0與拋物線交于不同的兩點(diǎn)A，B．點(diǎn)A關(guān)于y軸的對稱點(diǎn)為SKIPIF1<0，連接SKIPIF1<0．求證：直線SKIPIF1<0過y軸上一定點(diǎn)，并求出此定點(diǎn)坐標(biāo)．80．已知橢圓SKIPIF1<0的左?右頂點(diǎn)分別為A，B，右焦點(diǎn)為F，直線SKIPIF1<0.（1）若橢圓W的左頂點(diǎn)A關(guān)于直線SKIPIF1<0的對稱點(diǎn)在直線SKIPIF1<0上，求m的值；（2）過F的直線SKIPIF1<0與橢圓W相交于不同的兩點(diǎn)C，D（不與點(diǎn)A，B重合），直線SKIPIF1<0與直線SKIPIF1<0相交于點(diǎn)M，求證：A，D，M三點(diǎn)共線.81．已知拋物線SKIPIF1<0：SKIPIF1<0上有一點(diǎn)SKIPIF1<0.（1）求拋物線SKIPIF1<0的標(biāo)準(zhǔn)方程及其準(zhǔn)線方程；（2）過點(diǎn)SKIPIF1<0的直線交拋物線C于A，B兩點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，記直線OA，OB的斜率分別為SKIPIF1<0，SKIPIF1<0，求證：SKIPIF1<0為定值.82．已知橢圓SKIPIF1<0的左右頂點(diǎn)分別為A，B，點(diǎn)P為橢圓上異于A，B的任意一點(diǎn)．（1）證明：直線PA與直線PB的斜率乘積為定值；（2）設(shè)SKIPIF1<0，過點(diǎn)Q作與SKIPIF1<0軸不重合的任意直線交橢圓E于M，N兩點(diǎn)．問：是否存在實(shí)數(shù)SKIPIF1<0，使得以MN為直徑的圓恒過定點(diǎn)B？若存在，求出SKIPIF1<0的值；若不存在，請說明理由．83．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，且SKIPIF1<0為圓SKIPIF1<0的圓心．過SKIPIF1<0點(diǎn)的直線SKIPIF1<0交拋物線與圓分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0（從上到下）．（1）求拋物線方程并證明SKIPIF1<0是定值；（2）若SKIPIF1<0，SKIPIF1<0的面積比是SKIPIF1<0，求直線SKIPIF1<0的方程．84．如圖，已知橢圓C：SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0為其左右焦點(diǎn)，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0與橢圓C交于A、B兩點(diǎn)，點(diǎn)M為線段AB的中點(diǎn).（1）若直線SKIPIF1<0的斜率為2，求直線OM的斜率；（2）若SKIPIF1<0，求SKIPIF1<0的面積.85．已知橢圓SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，且橢圓E的離心率SKIPIF1<0．（1）求橢圓E的標(biāo)準(zhǔn)方程：（2）當(dāng)直線l（斜率不為0）經(jīng)過點(diǎn)F，且與橢圓E交于A、B兩點(diǎn)時(shí)，問x軸上是否存在定點(diǎn)P，使得x軸平分SKIPIF1<0？若存在，求出點(diǎn)P的坐標(biāo)；若不存在，請說明理由．86．若拋物線SKIPIF1<0的交點(diǎn)為F，過F作直線l與拋物線SKIPIF1<0交于A，B兩點(diǎn)，分別以線段AF，BF為直徑作圓SKIPIF1<0和圓SKIPIF1<0.（1）證明：圓SKIPIF1<0和圓SKIPIF1<0均與y軸相切；（2）設(shè)圓SKIPIF1<0與y軸相切于點(diǎn)D，圓SKIPIF1<0與y相切于點(diǎn)E，求SKIPIF1<0的值，并求SKIPIF1<0面積的最小值.87．已知橢圓SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，且點(diǎn)SKIPIF1<0為橢圓SKIPIF1<0上一點(diǎn).（1）求橢圓SKIPIF1<0的方程.（2）已知SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0交橢圓SKIPIF1<0于A，B兩點(diǎn)，證明：直線PA斜率與直線PB斜率之積為定值.88．已知拋物線C：SKIPIF1<0，直線l過拋物線焦點(diǎn)F，l與C有兩個(gè)交點(diǎn)A，B，線段AB的中點(diǎn)M的縱坐標(biāo)為1.（1）求直線l的方程；（2）求SKIPIF1<0（O為坐標(biāo)原點(diǎn)）的面積SKIPIF1<0.89．有一種畫橢圓的工具如圖1所示，定點(diǎn)O是滑槽AB的中點(diǎn)，短桿OP繞O轉(zhuǎn)動，長桿PQ通過P處鉸鏈與OP連接，PQ上的栓子D可沿滑槽AB滑動，且SKIPIF1<0，SKIPIF1<0．當(dāng)栓子D在滑槽AB內(nèi)作往復(fù)運(yùn)動時(shí)，帶動P繞O轉(zhuǎn)動一周（D不動時(shí)，P也不動），Q處的筆尖畫出的曲線記為C．以O(shè)為原點(diǎn)，AB所在的直線為x軸，建立如圖2所示的平面直角坐標(biāo)系．（1）求曲線C的方程；（2）在平面直角坐標(biāo)系xOy中，過點(diǎn)SKIPIF1<0的動直線l與曲線C交于E、F兩點(diǎn)，是否存在異于點(diǎn)M的定點(diǎn)N，使得MN平分SKIPIF1<0？若存在，求點(diǎn)N坐標(biāo)；若不存在，說明理由．90．已知橢圓SKIPIF1<0：SKIPIF1<0的右焦點(diǎn)SKIPIF1<0和上頂點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，過橢圓右焦點(diǎn)的直線交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn).（1）求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）求SKIPIF1<0面積的最大值.91．如圖，橢圓SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0分別是其左、右焦點(diǎn)，過SKIPIF1<0的直線SKIPIF1<0交橢圓于點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是橢圓上不與SKIPIF1<0，SKIPIF1<0重合的動點(diǎn)，SKIPIF1<0是坐標(biāo)原點(diǎn)．（1）若SKIPIF1<0是△SKIPIF1<0的外心，SKIPIF1<0，求SKIPIF1<0的值；（2）若SKIPIF1<0是△SKIPIF1<0的重心，求SKIPIF1<0的取值范圍．92．已知SKIPIF1<0的上頂點(diǎn)到右頂點(diǎn)的距離為SKIPIF1<0，離心率為SKIPIF1<0，過橢圓左焦點(diǎn)SKIPIF1<0作不與x軸重合的直線與橢圓C相交于M、N兩點(diǎn)，直線m的方程為：SKIPIF1<0，過點(diǎn)M作ME垂直于直線m于點(diǎn)E（1）求橢圓C的標(biāo)準(zhǔn)方程；（2）（i）求證：線段EN必過定點(diǎn)SKIPIF1<0，并求SKIPIF1<0的值（ii）點(diǎn)O為坐標(biāo)原點(diǎn)，求△OEN面積的最大值93．在直角坐標(biāo)系SKIPIF1<0中，橢圓SKIPIF1<0（SKIPIF1<0）的左右焦點(diǎn)分別為SKIPIF1<0和SKIPIF1<0，若SKIPIF1<0為橢圓上動點(diǎn)，直線SKIPIF1<0與橢圓交于另一點(diǎn)SKIPIF1<0，若三角形SKIPIF1<0的周長為為SKIPIF1<0，且點(diǎn)SKIPIF1<0在橢圓上．（1）求橢圓的標(biāo)準(zhǔn)方程；（2）設(shè)直線SKIPIF1<0、SKIPIF1<0與直線SKIPIF1<0分別交于點(diǎn)SKIPIF1<0、SKIPIF1<0，記直線SKIPIF