新高考數(shù)學(xué)一輪復(fù)習(xí)百題刷過(guò)關(guān)專題27 圓錐曲線點(diǎn)差法必刷100題(原卷版)

專題27圓錐曲線點(diǎn)差法必刷100題任務(wù)一:善良模式(基礎(chǔ))1-30題一、單選題1．已知雙曲線SKIPIF1<0被直線截得的弦AB，弦的中點(diǎn)為M（4，2），則直線AB的斜率為（）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．22．若點(diǎn)SKIPIF1<0為圓SKIPIF1<0的弦SKIPIF1<0的中點(diǎn)，則弦SKIPIF1<0所在直線的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)恰好為線段SKIPIF1<0的中點(diǎn)，則直線SKIPIF1<0的斜率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若直線l與橢圓SKIPIF1<0交于點(diǎn)A、B，線段AB中點(diǎn)P為（1，2），則直線l的斜率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．6 D．－65．過(guò)點(diǎn)SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，當(dāng)點(diǎn)SKIPIF1<0恰好為SKIPIF1<0的中點(diǎn)時(shí)，直線SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．以橢圓SKIPIF1<0內(nèi)一點(diǎn)SKIPIF1<0為中點(diǎn)的弦所在的直線方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知橢圓SKIPIF1<0(SKIPIF1<0)的右焦點(diǎn)為SKIPIF1<0，離心率為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則直線SKIPIF1<0的斜率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．18．已知直線l被雙曲線C：SKIPIF1<0﹣y2=1所截得的弦的中點(diǎn)坐標(biāo)為(1，2)，則直線l的方程（）A．x+4y﹣9=0 B．x﹣4y+7=0C．x﹣8y+15=0 D．x+8y﹣17=09．已知橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線交橢圓于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，則橢圓SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知橢圓SKIPIF1<0，點(diǎn)SKIPIF1<0為右焦點(diǎn)，SKIPIF1<0為上頂點(diǎn)，平行于SKIPIF1<0的直線SKIPIF1<0交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn)且線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則橢圓的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．在拋物線SKIPIF1<0中，以SKIPIF1<0為中點(diǎn)的弦所在直線的方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．已知斜率為SKIPIF1<0的直線與雙曲線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則雙曲線的漸近線方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．直線SKIPIF1<0經(jīng)過(guò)橢圓SKIPIF1<0的左焦點(diǎn)SKIPIF1<0，且與橢圓交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為線段SKIPIF1<0中點(diǎn)，SKIPIF1<0，則橢圓的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．已知曲線SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0且被點(diǎn)SKIPIF1<0平分的弦SKIPIF1<0所在的直線方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<015．過(guò)點(diǎn)SKIPIF1<0作斜率為SKIPIF1<0的直線與橢圓SKIPIF1<0：SKIPIF1<0(SKIPIF1<0)相交于SKIPIF1<0?SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則橢圓SKIPIF1<0的離心率等于（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．過(guò)橢圓SKIPIF1<0的右焦點(diǎn)SKIPIF1<0的直線與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若線段SKIPIF1<0的中點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．已知斜率為SKIPIF1<0SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，直線SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）的斜率為SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<018．過(guò)點(diǎn)SKIPIF1<0作斜率為SKIPIF1<0的直線與橢圓SKIPIF1<0：SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則橢圓SKIPIF1<0的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0第II卷（非選擇題）二、填空題19．已知橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，則橢圓SKIPIF1<0的方程為_(kāi)__________．20．橢圓SKIPIF1<0離心率為SKIPIF1<0，直線SKIPIF1<0與橢圓交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0中點(diǎn)為SKIPIF1<0，SKIPIF1<0為原點(diǎn)，則直線SKIPIF1<0的斜率是_______．21．已知SKIPIF1<0為拋物線SKIPIF1<0的一條長(zhǎng)度為8的弦，當(dāng)弦SKIPIF1<0的中點(diǎn)離SKIPIF1<0軸最近時(shí)，直線SKIPIF1<0的斜率為_(kāi)__________.22．直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，設(shè)直線SKIPIF1<0的斜率為SKIPIF1<0，直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0______．23．已知橢圓SKIPIF1<0，過(guò)點(diǎn)（4，0）的直線交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn).若SKIPIF1<0中點(diǎn)坐標(biāo)為（2，﹣1），則橢圓SKIPIF1<0的離心率為_(kāi)______24．設(shè)SKIPIF1<0、SKIPIF1<0是拋物線SKIPIF1<0上不同的兩點(diǎn)，線段SKIPIF1<0的垂直平分線為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0______.25．已知直線SKIPIF1<0與橢圓SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0中點(diǎn)的橫坐標(biāo)恰好為SKIPIF1<0，則橢圓SKIPIF1<0的離心率為_(kāi)_____.26．在直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0是圓SKIPIF1<0的弦，SKIPIF1<0是SKIPIF1<0中點(diǎn)，若SKIPIF1<0，SKIPIF1<0都存在非零斜率SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0.類比于圓，在直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0是橢圓SKIPIF1<0的弦，SKIPIF1<0是SKIPIF1<0中點(diǎn)，若SKIPIF1<0，SKIPIF1<0都存在非零斜率SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0________.三、解答題27．已知橢圓SKIPIF1<0：SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，長(zhǎng)軸長(zhǎng)為SKIPIF1<0.（1）求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）過(guò)點(diǎn)SKIPIF1<0作直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，當(dāng)SKIPIF1<0為線段SKIPIF1<0中點(diǎn)時(shí)，求直線SKIPIF1<0的方程.28．已知橢圓C的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，過(guò)SKIPIF1<0的直線與橢圓C交于A，B兩點(diǎn).若SKIPIF1<0的周長(zhǎng)為SKIPIF1<0.（1）求橢圓C的方程；（2）橢圓SKIPIF1<0中以SKIPIF1<0為中點(diǎn)的弦所在直線方程.29．設(shè)橢圓SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，離心率為SKIPIF1<0（1）求C的方程；（2）求過(guò)點(diǎn)SKIPIF1<0且以M點(diǎn)為中點(diǎn)的弦的方程．30．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上的兩個(gè)點(diǎn)，點(diǎn)SKIPIF1<0是線段SKIPIF1<0的中點(diǎn).（1）求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）求SKIPIF1<0.任務(wù)二:中立模式(中檔)1-40題一、單選題1．已知橢圓C：SKIPIF1<0上存在兩點(diǎn)M，N關(guān)于直線SKIPIF1<0對(duì)稱，且線段MN中點(diǎn)的縱坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．22．設(shè)直線SKIPIF1<0與雙曲線SKIPIF1<0兩條漸近線分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0，若點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則該雙曲線的漸近線方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知橢圓SKIPIF1<0：SKIPIF1<0上有三點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，線段SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的中點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的斜率都存在，分別記為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的斜率都存在，分別記為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．斜率為SKIPIF1<0的直線SKIPIF1<0經(jīng)過(guò)雙曲線SKIPIF1<0的左焦點(diǎn)SKIPIF1<0，交雙曲線于SKIPIF1<0兩點(diǎn)，SKIPIF1<0為雙曲線的右焦點(diǎn)且SKIPIF1<0，則雙曲線的漸近線方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知橢圓SKIPIF1<0：SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0作一條傾斜角為SKIPIF1<0的直線與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，若SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），則橢圓SKIPIF1<0的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．直線l與拋物線SKIPIF1<0相交于A，B兩點(diǎn)，線段AB的中點(diǎn)為M，點(diǎn)P是y軸左側(cè)一點(diǎn)，若線段PA，PB的中點(diǎn)都在拋物線上，則（）A．PM與y軸垂直 B．PM的中點(diǎn)在拋物線上C．PM必過(guò)原點(diǎn) D．PA與PB垂直7．已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，SKIPIF1<0，則直線SKIPIF1<0的斜率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知橢圓SKIPIF1<0（SKIPIF1<0）的右焦點(diǎn)為SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線交橢圓于A，SKIPIF1<0兩點(diǎn)，若線段SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，則橢圓SKIPIF1<0的方程為（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．拋物線SKIPIF1<0上有一動(dòng)弦SKIPIF1<0，中點(diǎn)為SKIPIF1<0，且弦SKIPIF1<0的長(zhǎng)為3，則點(diǎn)SKIPIF1<0的縱坐標(biāo)的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．110．過(guò)點(diǎn)SKIPIF1<0作直線l與雙曲線SKIPIF1<0交于P，Q兩點(diǎn)，且使得A是SKIPIF1<0的中點(diǎn)，直線l方程為（）A．SKIPIF1<0 B．2x+y-3=0 C．x=1 D．不存在11．以原點(diǎn)為對(duì)稱中心的橢圓SKIPIF1<0焦點(diǎn)分別在SKIPIF1<0軸，SKIPIF1<0軸，離心率分別為SKIPIF1<0，直線SKIPIF1<0交SKIPIF1<0所得的弦中點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則直線SKIPIF1<0的斜率為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．過(guò)橢圓SKIPIF1<0的右焦點(diǎn)SKIPIF1<0并垂直于SKIPIF1<0軸的直線與橢圓的一個(gè)交點(diǎn)為SKIPIF1<0，橢圓上不同的兩點(diǎn)SKIPIF1<0，滿足條件：SKIPIF1<0成等差數(shù)列，則弦SKIPIF1<0的中垂線在SKIPIF1<0軸上的截距的范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．已知橢圓SKIPIF1<0的右焦點(diǎn)和上頂點(diǎn)分別為點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0，直線SKIPIF1<0交橢圓于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0恰好為SKIPIF1<0的重心，則橢圓的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．已知圓SKIPIF1<0在橢圓SKIPIF1<0的內(nèi)部，點(diǎn)SKIPIF1<0為SKIPIF1<0上一動(dòng)點(diǎn).過(guò)SKIPIF1<0作圓SKIPIF1<0的一條切線，交SKIPIF1<0于另一點(diǎn)SKIPIF1<0，切點(diǎn)為SKIPIF1<0，當(dāng)SKIPIF1<0為SKIPIF1<0的中點(diǎn)時(shí)，直線SKIPIF1<0的斜率為SKIPIF1<0，則SKIPIF1<0的離心率為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知雙曲線SKIPIF1<0：SKIPIF1<0，若存在斜率為1的直線與SKIPIF1<0的左?右兩支分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0，且線段SKIPIF1<0的中點(diǎn)在圓SKIPIF1<0：SKIPIF1<0上，則SKIPIF1<0的離心率的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<016．過(guò)拋物線SKIPIF1<0的焦點(diǎn)F的直線l（不平行于y軸）交拋物線于A，B兩點(diǎn)，線段AB的中垂線交x軸于點(diǎn)M，若SKIPIF1<0，則線段FM的長(zhǎng)度為（）A．1 B．2 C．3 D．417．已知拋物線C1：SKIPIF1<0和圓C2：(x-6)2+(y-1)2=1，過(guò)圓C2上一點(diǎn)P作圓的切線MN交拋物線C，于M，N兩點(diǎn)，若點(diǎn)P為MN的中點(diǎn)，則切線MN的斜率k>1時(shí)的直線方程為（）A．4x-3y-22=0 B．4x-3y-16=0 C．2x-y-11+5=0 D．4x-3y-26=018．已知圓SKIPIF1<0與橢圓SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是圓SKIPIF1<0的直徑，則橢圓SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<019．已知拋物線SKIPIF1<0，直線SKIPIF1<0交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，SKIPIF1<0是SKIPIF1<0的中點(diǎn)，過(guò)SKIPIF1<0作SKIPIF1<0軸的垂線交拋物線SKIPIF1<0于點(diǎn)SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則k為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．220．已知橢圓SKIPIF1<0上存在兩點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，且線段SKIPIF1<0中點(diǎn)的縱坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0第II卷（非選擇題）二、填空題21．已知斜率為1的直線l與雙曲線C：SKIPIF1<0相交于B，D兩點(diǎn)，且BD的中點(diǎn)為SKIPIF1<0，則C的離心率是______．22．已知橢圓SKIPIF1<0的弦被點(diǎn)SKIPIF1<0平分，則這條弦所在的直線方程為_(kāi)_____.23．已知橢圓SKIPIF1<0離心率SKIPIF1<0，過(guò)橢圓中心的直線交橢圓于A、B兩點(diǎn)（A在第一象限），過(guò)A作x軸垂線交橢圓于點(diǎn)C，過(guò)A作直線AP垂直AB交橢圓于點(diǎn)P，連接BP交AC于點(diǎn)Q，則SKIPIF1<0____24．已知橢圓SKIPIF1<0：SKIPIF1<0上存在SKIPIF1<0，SKIPIF1<0兩點(diǎn)關(guān)于直線SKIPIF1<0對(duì)稱，且線段SKIPIF1<0的中點(diǎn)在拋物線SKIPIF1<0上，則實(shí)數(shù)SKIPIF1<0的值為_(kāi)__________.25．已知橢圓SKIPIF1<0：SKIPIF1<0SKIPIF1<0的左焦點(diǎn)為SKIPIF1<0，過(guò)SKIPIF1<0作一條傾斜角為SKIPIF1<0的直線與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，則橢圓SKIPIF1<0的離心率是___________.26．已知直線SKIPIF1<0與橢圓SKIPIF1<0交于A、B兩點(diǎn)，與圓SKIPIF1<0交于C、D兩點(diǎn)．若存在SKIPIF1<0，使得SKIPIF1<0，則橢圓SKIPIF1<0的離心率的取值范圍是_____________．27．橢圓SKIPIF1<0內(nèi)，過(guò)點(diǎn)SKIPIF1<0且被該點(diǎn)平分的弦所在的直線方程為_(kāi)_____．28．已知圓SKIPIF1<0：SKIPIF1<0與橢圓SKIPIF1<0：SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0是圓SKIPIF1<0的直徑，則橢圓SKIPIF1<0的方程為_(kāi)_______.29．已知SKIPIF1<0為橢圓SKIPIF1<0的右焦點(diǎn).直線SKIPIF1<0與橢圓C相交于A，B兩點(diǎn)，A，B的中點(diǎn)為P，且直線OP的斜率SKIPIF1<0，則橢圓C的方程為_(kāi)______________.30．已知曲線SKIPIF1<0：SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0在曲線SKIPIF1<0上，且以SKIPIF1<0為直徑的圓的方程是SKIPIF1<0．則SKIPIF1<0______．31．已知拋物線E：y2＝4x，A（x1，y1），B（x2，y2），C（x3，y3）為拋物線上的三個(gè)動(dòng)點(diǎn)，其中x1＜x2＜x3且y2＜0，若SKIPIF1<0ABC的重心恰為拋物線E的焦點(diǎn)，且AB、AC、BC三邊中點(diǎn)到拋物線E的準(zhǔn)線的距離成等差數(shù)列，則直線AC的斜率為_(kāi)____.32．已知橢圓SKIPIF1<0，作傾斜角為SKIPIF1<0的直線交橢圓C于A、B兩點(diǎn)，線段SKIPIF1<0的中點(diǎn)M，O為坐標(biāo)原點(diǎn)，SKIPIF1<0與SKIPIF1<0的夾角為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0____________33．已知拋物線SKIPIF1<0的準(zhǔn)線方程為SKIPIF1<0，在拋物線SKIPIF1<0上存在兩點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，且SKIPIF1<0為坐標(biāo)原點(diǎn)，則SKIPIF1<0的值為_(kāi)_________.34．已知橢圓C：SKIPIF1<0的一個(gè)頂點(diǎn)為SKIPIF1<0，離心率SKIPIF1<0，直線SKIPIF1<0交橢圓于M，N兩點(diǎn)，如果△BMN的重心恰好為橢圓的左焦點(diǎn)F，則直線SKIPIF1<0方程為_(kāi)__________35．已知拋物線SKIPIF1<0上一點(diǎn)SKIPIF1<0到焦點(diǎn)SKIPIF1<0的距離為3，過(guò)焦點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0，當(dāng)SKIPIF1<0取得最大值時(shí)，SKIPIF1<0的面積等于__________．三、解答題36．已知拋物線SKIPIF1<0的焦點(diǎn)為F，過(guò)F且斜率為1的直線與拋物線C交于A，B兩點(diǎn)，且SKIPIF1<0的中點(diǎn)的縱坐標(biāo)為2．（1）求C的方程（2）已知SKIPIF1<0，若P在線段SKIPIF1<0上，SKIPIF1<0是拋物線C的兩條切線，切點(diǎn)為H，G，求SKIPIF1<0面積的最大值．37．已知橢圓SKIPIF1<0：SKIPIF1<0，直線SKIPIF1<0不過(guò)原點(diǎn)SKIPIF1<0且不平行于坐標(biāo)軸，SKIPIF1<0與SKIPIF1<0有兩個(gè)交點(diǎn)SKIPIF1<0，SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0.（1）證明：直線SKIPIF1<0的斜率與SKIPIF1<0的斜率的乘積為定值；（2）若SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，射線SKIPIF1<0與橢圓SKIPIF1<0交于點(diǎn)SKIPIF1<0，四邊形SKIPIF1<0能否為平行四邊形？若能，求此時(shí)直線SKIPIF1<0斜率；若不能，說(shuō)明理由.38．在平面直角坐標(biāo)系xOy中，已知橢圓C：SKIPIF1<0（a>b>0）的離心率為SKIPIF1<0，AB為橢圓的一條弦，直線y=kx（k>0）經(jīng)過(guò)弦AB的中點(diǎn)M，與橢圓C交于P，Q兩點(diǎn)，設(shè)直線AB的斜率為SKIPIF1<0，點(diǎn)P的坐標(biāo)為（1，SKIPIF1<0）（1）求橢圓C的方程；（2）求證：SKIPIF1<0為定值.39．已知SKIPIF1<0，直線SKIPIF1<0不過(guò)原點(diǎn)SKIPIF1<0且不平行于坐標(biāo)軸，SKIPIF1<0與SKIPIF1<0有兩個(gè)交點(diǎn)SKIPIF1<0，線段SKIPIF1<0中點(diǎn)為SKIPIF1<0.（1）若SKIPIF1<0，點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，SKIPIF1<0分別為橢圓的兩個(gè)焦點(diǎn)，求SKIPIF1<0的取值范圍；（2）若SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，射線SKIPIF1<0與橢圓SKIPIF1<0交于點(diǎn)SKIPIF1<0，四邊形SKIPIF1<0能否為平行四邊形？若能，求出此時(shí)直線SKIPIF1<0的斜率；若不能，請(qǐng)說(shuō)明理由.40．已知橢圓SKIPIF1<0，試確定m的取值范圍，使得圓E上存在不同的兩點(diǎn)關(guān)于直線SKIPIF1<0對(duì)稱.任務(wù)三:邪惡模式(困難)1-30題一、解答題1．已知SKIPIF1<0的兩個(gè)頂點(diǎn)坐標(biāo)分別為SKIPIF1<0，該三角形的內(nèi)切圓與邊SKIPIF1<0分別相切于P，Q，S三點(diǎn)，且SKIPIF1<0，設(shè)SKIPIF1<0的頂點(diǎn)A的軌跡為曲線E．（1）求E的方程；（2）直線SKIPIF1<0交E于R，V兩點(diǎn)．在線段SKIPIF1<0上任取一點(diǎn)T，過(guò)T作直線SKIPIF1<0與E交于M，N兩點(diǎn)，并使得T是線段SKIPIF1<0的中點(diǎn)，試比較SKIPIF1<0與SKIPIF1<0的大小并加以證明．2．已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且橢圓SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，離心率SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，過(guò)SKIPIF1<0且不平行于坐標(biāo)軸的動(dòng)直線SKIPIF1<0與SKIPIF1<0有兩個(gè)交點(diǎn)SKIPIF1<0，SKIPIF1<0，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0.（1）求SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）記直線SKIPIF1<0的斜率為SKIPIF1<0，直線SKIPIF1<0的斜率為SKIPIF1<0，證明：SKIPIF1<0為定值；（3）SKIPIF1<0軸上是否存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0為等邊三角形？若存在，求出點(diǎn)SKIPIF1<0的坐標(biāo)；若不存在，請(qǐng)說(shuō)明理由.3．已知點(diǎn)SKIPIF1<0，不垂直于x軸的直線l與橢圓SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)．（1）若M為線段SKIPIF1<0的中點(diǎn)，證明：SKIPIF1<0；（2）設(shè)C的左焦點(diǎn)為F，若M在SKIPIF1<0的角平分線所在直線上，且l被圓SKIPIF1<0截得的弦長(zhǎng)為SKIPIF1<0，求l的方程．4．已知點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，且點(diǎn)M到C的左?右焦點(diǎn)的距離之和為SKIPIF1<0.（1）求C的方程；（2）設(shè)О為坐標(biāo)原點(diǎn)，若C的弦AB的中點(diǎn)在線段OM(不含端點(diǎn)O，M)上，求SKIPIF1<0的取值范圍.5．已知橢圓SKIPIF1<0：SKIPIF1<0.（1）橢圓SKIPIF1<0是否存在以點(diǎn)SKIPIF1<0為中點(diǎn)的弦？若存在，求出弦所在的直線SKIPIF1<0的方程，若不存在，請(qǐng)說(shuō)明理由；（2）已知橢圓SKIPIF1<0的左?右頂點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0上的點(diǎn)，若直線SKIPIF1<0，SKIPIF1<0分別與直線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，求線段SKIPIF1<0的長(zhǎng)度取得最小值時(shí)直線SKIPIF1<0的斜率.6．已知斜率為的SKIPIF1<0的直線SKIPIF1<0與橢圓SKIPIF1<0交于點(diǎn)SKIPIF1<0，線段SKIPIF1<0中點(diǎn)為SKIPIF1<0，直線SKIPIF1<0在SKIPIF1<0軸上的截距為橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)的SKIPIF1<0倍.（1）求橢圓SKIPIF1<0的方程；（2）若點(diǎn)SKIPIF1<0都在橢圓上，且SKIPIF1<0都經(jīng)過(guò)橢圓SKIPIF1<0的右焦點(diǎn)SKIPIF1<0，設(shè)直線SKIPIF1<0的斜率分別為SKIPIF1<0，SKIPIF1<0，線段PQ,MN的中點(diǎn)分別為SKIPIF1<0，判斷直線SKIPIF1<0是否過(guò)定點(diǎn)，若過(guò)定點(diǎn).求出該定點(diǎn)，若不過(guò)定點(diǎn)，說(shuō)明理由.7．已知拋物線SKIPIF1<0，過(guò)其焦點(diǎn)且斜率為SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若線段SKIPIF1<0的中點(diǎn)的縱坐標(biāo)為SKIPIF1<0．（1）求拋物線SKIPIF1<0的方程；（2）若點(diǎn)SKIPIF1<0，問(wèn)x軸上是否存在點(diǎn)SKIPIF1<0，使得過(guò)點(diǎn)SKIPIF1<0的任一條直線與拋物線SKIPIF1<0交于點(diǎn)SKIPIF1<0兩點(diǎn)，且點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離相等？若存在，求出點(diǎn)SKIPIF1<0的坐標(biāo)；若不存在，說(shuō)明理由．8．如圖，曲線SKIPIF1<0由兩個(gè)橢圓SKIPIF1<0和橢圓SKIPIF1<0組成，當(dāng)a、b、c成等比數(shù)列時(shí)，稱曲線SKIPIF1<0為“貓眼曲線”，若貓眼曲線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，且a、b、c的公比為SKIPIF1<0.（1）求貓眼曲線SKIPIF1<0的方程；（2）任作斜率為SKIPIF1<0且不過(guò)原點(diǎn)的直線與該曲線SKIPIF1<0相交，交橢圓SKIPIF1<0所得弦AB的中點(diǎn)為M，交橢圓SKIPIF1<0所得弦CD的中點(diǎn)為N，直線OM、直線ON的斜率分別為SKIPIF1<0、SKIPIF1<0，求證：SKIPIF1<0為與k無(wú)關(guān)的定值；（3）設(shè)SKIPIF1<0、SKIPIF1<0為橢圓SKIPIF1<0上的兩點(diǎn)，直線OP、直線SKIPIF1<0的斜率分別為SKIPIF1<0、SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的最大值.9．坐標(biāo)平面內(nèi)的動(dòng)圓SKIPIF1<0與圓SKIPIF1<0SKIPIF1<0外切，與圓SKIPIF1<0內(nèi)切，設(shè)動(dòng)圓SKIPIF1<0的圓心SKIPIF1<0的軌跡是曲線SKIPIF1<0，直線SKIPIF1<0SKIPIF1<0.（1）求曲線SKIPIF1<0的方程；（2）當(dāng)點(diǎn)SKIPIF1<0在曲線SKIPIF1<0上運(yùn)動(dòng)時(shí)，它到直線SKIPIF1<0的距離最??？最小值距離是多少？（3）一組平行于直線SKIPIF1<0的直線，當(dāng)它們與曲線SKIPIF1<0相交時(shí)，試判斷這些直線被橢圓所截得的線段的中點(diǎn)是否在同一條直線上，若在同一條直線上，求出該直線的方程；若不在同一條直線上，請(qǐng)說(shuō)明理由？10．已知點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）上，且點(diǎn)SKIPIF1<0到SKIPIF1<0的左、右焦點(diǎn)的距離之和為SKIPIF1<0.（1）求SKIPIF1<0的方程；（2）設(shè)SKIPIF1<0為坐標(biāo)原點(diǎn)，若SKIPIF1<0的弦SKIPIF1<0的中點(diǎn)在線段SKIPIF1<0（不含端點(diǎn)SKIPIF1<0，SKIPIF1<0）上，求SKIPIF1<0的取值范圍.11．如圖，橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，過(guò)焦點(diǎn)SKIPIF1<0，斜率為SKIPIF1<0的直線SKIPIF1<0交橢圓于SKIPIF1<0、SKIPIF1<0兩點(diǎn)（異于長(zhǎng)軸端點(diǎn)），SKIPIF1<0是直線SKIPIF1<0上的動(dòng)點(diǎn)．（1）若直線SKIPIF1<0平分線段SKIPIF1<0，求證：SKIPIF1<0．（2）若直線SKIPIF1<0的斜率SKIPIF1<0，直線SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的斜率成等差數(shù)列，求實(shí)數(shù)SKIPIF1<0的取值范圍．12．在平面直角坐標(biāo)系中，已知橢圓SKIPIF1<0，直線SKIPIF1<0．（1）若橢圓C的一條準(zhǔn)線方程為SKIPIF1<0，且焦距為2，求橢圓C的方程；（2）設(shè)橢圓C的左焦點(diǎn)為F，上頂點(diǎn)為A，直線l過(guò)點(diǎn)F，且與FA垂直，交橢圓C于M，N（M在x軸上方），若SKIPIF1<0，求橢圓C的離心率；（3）在（1）的條件下，若橢圓C上存在相異兩點(diǎn)P，Q關(guān)于直線l對(duì)稱，求SKIPIF1<0的取值范圍（用k表示）．13．在平面直角坐標(biāo)系SKIPIF1<0中，橢圓SKIPIF1<0的離心率為SKIPIF1<0，左、右頂點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，且線段SKIPIF1<0的長(zhǎng)為SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0異于頂點(diǎn)SKIPIF1<0，SKIPIF1<0的點(diǎn)，過(guò)點(diǎn)SKIPIF1<0，SKIPIF1<0分別作SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0交于點(diǎn)SKIPIF1<0．（1）求橢圓SKIPIF1<0的方程；（2）求證：當(dāng)SKIPIF1<0在橢圓SKIPIF1<0上運(yùn)動(dòng)時(shí)，點(diǎn)SKIPIF1<0恒在一定橢圓SKIPIF1<0上；（3）已知直線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，且與（2）中的橢圓SKIPIF1<0交于不同的兩點(diǎn)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，求原點(diǎn)SKIPIF1<0到直線SKIPIF1<0距離的最小值．14．在平面直角坐標(biāo)系SKIPIF1<0中，已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，SKIPIF1<0為橢圓的一條弦（不經(jīng)過(guò)原點(diǎn)），直線SKIPIF1<0經(jīng)過(guò)弦SKIPIF1<0的中點(diǎn)，與橢圓SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，設(shè)直線SKIPIF1<0的斜率為SKIPIF1<0.（1）若點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，求橢圓SKIPIF1<0的方程；（2）求證：SKIPIF1<0為定值；（3）過(guò)SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為SKIPIF1<0，若直線SKIPIF1<0和直線SKIPIF1<0傾斜角互補(bǔ)，且SKIPIF1<0的面積為SKIPIF1<0，求橢圓SKIPIF1<0的方程.15．已知橢圓SKIPIF1<0的右焦點(diǎn)為SKIPIF1<0，右準(zhǔn)線為SKIPIF1<0.過(guò)點(diǎn)SKIPIF1<0作與坐標(biāo)軸都不垂直的直線與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，且直線SKIPIF1<0與右準(zhǔn)線SKIPIF1<0交于點(diǎn)SKIPIF1<0.（1）求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；（2）若SKIPIF1<0，求直線SKIPIF1<0的方程；（3）是否存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0恒成立？若存在，求實(shí)數(shù)SKIPIF1<0的值；若不存在，請(qǐng)說(shuō)明理由.16．SKIPIF1<0為坐標(biāo)原點(diǎn)，橢圓SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，橢圓SKIPIF1<0的右頂點(diǎn)為SKIPIF1<0.設(shè)SKIPIF1<0，SKIPIF1<0是SKIPIF1<0上位于第二象限的兩點(diǎn)，且滿足SKIPIF1<0，SKIPIF1<0是弦SKIPIF1<0的中點(diǎn)，射線SKIPIF1<0與橢圓交于點(diǎn)SKIPIF1<0.（1）求證：直線SKIPIF1<0與直線SKIPIF1<0斜率的乘積為SKIPIF1<0；（2）若SKIPIF1<0，求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程.17．已知SKIPIF1<0是曲線SKIPIF1<0上的動(dòng)點(diǎn)，且點(diǎn)SKIPIF1<0到SKIPIF1<0的距離比它到x軸的距離大1.直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)為SKIPIF1<0.（1）求曲線SKIPIF1<0的軌跡方程；（2）已知SKIPIF1<0是曲線SKIPIF1<0上不同的兩點(diǎn)，線段SKIPIF1<0的垂直垂直平分線交曲線SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則是否存在點(diǎn)S