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26 圓錐曲線中的弦長(zhǎng)問(wèn)題(原卷版)

專題26圓錐曲線中的弦長(zhǎng)問(wèn)題考試時(shí)間：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．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，若直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，則SKIPIF1<0（

）A．4 B．5 C．6 D．72．過(guò)拋物線SKIPIF1<0的焦點(diǎn)F作傾斜角為SKIPIF1<0的弦AB，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．直線SKIPIF1<0被橢圓SKIPIF1<0截得最長(zhǎng)的弦為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知橢圓SKIPIF1<0的左、右頂點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0不在坐標(biāo)軸上，直線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與直線SKIPIF1<0將于點(diǎn)SKIPIF1<0．設(shè)直線SKIPIF1<0的斜率為SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的所有值的和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知橢圓SKIPIF1<0的左?右頂點(diǎn)分別為SKIPIF1<0，點(diǎn)SKIPIF1<0為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0不在坐標(biāo)軸上，直線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與直線SKIPIF1<0將于點(diǎn)SKIPIF1<0.設(shè)直線SKIPIF1<0的斜率為SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的所有值的和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知圓SKIPIF1<0，若直線m過(guò)SKIPIF1<0且與圓交于SKIPIF1<0兩點(diǎn)，則弦長(zhǎng)SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．4 C．SKIPIF1<0 D．SKIPIF1<07．已知拋物線SKIPIF1<0：SKIPIF1<0(SKIPIF1<0)的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線為SKIPIF1<0，過(guò)SKIPIF1<0的直線交拋物線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，作SKIPIF1<0，SKIPIF1<0，垂足分別為SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．4 C．5 D．SKIPIF1<08．過(guò)橢圓SKIPIF1<0SKIPIF1<0上的焦點(diǎn)SKIPIF1<0作兩條相互垂直的直線SKIPIF1<0，SKIPIF1<0交橢圓于SKIPIF1<0兩點(diǎn)，SKIPIF1<0交橢圓于SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．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．已知橢圓SKIPIF1<0：SKIPIF1<0內(nèi)一點(diǎn)SKIPIF1<0，直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且點(diǎn)SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則（

）A．橢圓SKIPIF1<0的焦點(diǎn)坐標(biāo)為SKIPIF1<0，SKIPIF1<0B．橢圓SKIPIF1<0的長(zhǎng)軸長(zhǎng)為4C．直線SKIPIF1<0的方程為SKIPIF1<0D．SKIPIF1<010．已知SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是拋物線SKIPIF1<0上兩點(diǎn)，SKIPIF1<0為其焦點(diǎn)，則下列說(shuō)法正確的有（

）A．SKIPIF1<0周長(zhǎng)的最小值為SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0最小值為SKIPIF1<0C．若直線SKIPIF1<0過(guò)點(diǎn)SKIPIF1<0，則直線SKIPIF1<0，SKIPIF1<0的斜率之積恒為SKIPIF1<0D．若SKIPIF1<0外接圓與拋物線SKIPIF1<0的準(zhǔn)線相切，則該圓面積為SKIPIF1<011．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，其準(zhǔn)線SKIPIF1<0與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，過(guò)SKIPIF1<0的直線與SKIPIF1<0在第一象限內(nèi)自下而上依次交于SKIPIF1<0兩點(diǎn)，過(guò)SKIPIF1<0作SKIPIF1<0于SKIPIF1<0，則（

）A．SKIPIF1<0的方程為SKIPIF1<0B．當(dāng)SKIPIF1<0三點(diǎn)共線時(shí)，SKIPIF1<0C．SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<012．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，定點(diǎn)SKIPIF1<0和動(dòng)點(diǎn)SKIPIF1<0，SKIPIF1<0都在拋物線SKIPIF1<0上，且SKIPIF1<0（其中SKIPIF1<0為坐標(biāo)原點(diǎn)）的面積為3，則下列說(shuō)法正確的是（

）A．拋物線的標(biāo)準(zhǔn)方程為SKIPIF1<0B．設(shè)點(diǎn)SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，則點(diǎn)SKIPIF1<0的軌跡方程為SKIPIF1<0C．若SKIPIF1<0（點(diǎn)SKIPIF1<0在第一象限），則直線SKIPIF1<0的傾斜角為SKIPIF1<0D．若弦SKIPIF1<0的中點(diǎn)SKIPIF1<0的橫坐標(biāo)2，則SKIPIF1<0弦長(zhǎng)的最大值為7三、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．已知直線SKIPIF1<0與橢圓SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，則線段SKIPIF1<0的長(zhǎng)為．14．已知拋物線C：SKIPIF1<0（SKIPIF1<0）的焦點(diǎn)F與SKIPIF1<0的一個(gè)焦點(diǎn)重合，過(guò)焦點(diǎn)F的直線與C交于A，B兩不同點(diǎn)，拋物線C在A，B兩點(diǎn)處的切線相交于點(diǎn)M，且M的橫坐標(biāo)為4，則弦長(zhǎng)SKIPIF1<0．15．如果SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0是雙曲線左支上過(guò)點(diǎn)SKIPIF1<0的弦，且SKIPIF1<0，則SKIPIF1<0的周長(zhǎng)是16．已知斜率為SKIPIF1<0的直線SKIPIF1<0經(jīng)過(guò)拋物線SKIPIF1<0的焦點(diǎn)且與此拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0．直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0兩點(diǎn)在SKIPIF1<0軸的兩側(cè)．若SKIPIF1<0，則SKIPIF1<0．四、解答題：本大題共6小題，共70分.解答應(yīng)寫出必要的文字說(shuō)明、證明過(guò)程或演算步驟．17．已知橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程為SKIPIF1<0.(1)求橢圓SKIPIF1<0被直線SKIPIF1<0截得的弦長(zhǎng)；(2)若直線SKIPIF1<0與橢圓交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，當(dāng)SKIPIF1<0（O為坐標(biāo)原點(diǎn)）時(shí)，求SKIPIF1<0的值.18．已知O是平面直角坐標(biāo)系的原點(diǎn)，F(xiàn)是拋物線SKIPIF1<0：SKIPIF1<0的焦點(diǎn)，過(guò)點(diǎn)F的直線交拋物線于A，B兩點(diǎn)，且SKIPIF1<0的重心為G在曲線SKIPIF1<0上.(1)求拋物線C的方程；(2)記曲線SKIPIF1<0與y軸的交點(diǎn)為D，且直線AB與x軸相交于點(diǎn)E，弦AB的中點(diǎn)為M，求四邊形DEMG的面積最小值.19．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，右焦點(diǎn)為F，且E上一點(diǎn)P到F的最大距離3．（1）求橢圓E的方程；（2）若A，B為橢圓E上的兩點(diǎn)，線段AB過(guò)點(diǎn)F，且其垂直平分線交x軸于H點(diǎn)，SKIPIF1<0SKIPIF1<0，求SKIPIF1<0．20．已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動(dòng)，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0軸的垂線段SKIPIF1<0為垂足，SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)（當(dāng)點(diǎn)SKIPIF1<0經(jīng)過(guò)圓與SKIPIF1<0軸的交點(diǎn)時(shí)，規(guī)定點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0重合）．(1)求點(diǎn)SKIPIF1<0的軌跡方程；(2)經(jīng)過(guò)點(diǎn)SKIPIF1<0作直線SKIPIF1<0，與圓SKIPIF1<0相交于SKIPIF1<0