新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第27練 橢圓（原卷版）

第27練橢圓學(xué)校____________姓名____________班級____________一、單選題1．橢圓SKIPIF1<0的長半軸長SKIPIF1<0（

）A．11 B．7 C．5 D．22．已知橢圓SKIPIF1<0，則該橢圓的離心率SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．點(diǎn)P為橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0，SKIPIF1<0為該橢圓的兩個焦點(diǎn)，若SKIPIF1<0，則SKIPIF1<0（

）A．13 B．1 C．7 D．54．雙曲線E與橢圓SKIPIF1<0焦點(diǎn)相同且離心率是橢圓C離心率的SKIPIF1<0倍，則雙曲線E的標(biāo)準(zhǔn)方程為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0，SKIPIF1<0是橢圓SKIPIF1<0的兩個焦點(diǎn)，點(diǎn)M在橢圓C上，則SKIPIF1<0的最大值為（

）A．13 B．12 C．9 D．66．已知橢圓SKIPIF1<0的離心率為SKIPIF1<0，則橢圓E的長軸長為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上運(yùn)動，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上運(yùn)動，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．5 D．68．已知SKIPIF1<0分別是橢圓SKIPIF1<0的左、右焦點(diǎn)，點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在橢圓SKIPIF1<0上，SKIPIF1<0，SKIPIF1<0分別是SKIPIF1<0的中點(diǎn)，且SKIPIF1<0的周長為SKIPIF1<0，則橢圓SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知點(diǎn)SKIPIF1<0是橢圓SKIPIF1<0+SKIPIF1<0=1上的動點(diǎn)（點(diǎn)SKIPIF1<0不在坐標(biāo)軸上），SKIPIF1<0為橢圓的左，右焦點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)；若SKIPIF1<0是SKIPIF1<0的角平分線上的一點(diǎn)，且SKIPIF1<0丄SKIPIF1<0，則丨SKIPIF1<0丨的取值范圍為（

）A．（0，SKIPIF1<0） B．（0，2）C．（l，2） D．（SKIPIF1<0，2）10．已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0的直線交橢圓于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的最大值為10，則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題11．點(diǎn)SKIPIF1<0，SKIPIF1<0為橢圓C的兩個焦點(diǎn)，若橢圓C上存在點(diǎn)P，使得SKIPIF1<0，則橢圓C方程可以是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)P在橢圓C上，若方程SKIPIF1<0所表示的直線恒過定點(diǎn)M，點(diǎn)Q在以點(diǎn)M為圓心，C的長軸長為直徑的圓上，則下列說法正確的是（

）A．橢圓C的離心率為SKIPIF1<0 B．SKIPIF1<0的最大值為4C．SKIPIF1<0的面積可能為2 D．SKIPIF1<0的最小值為SKIPIF1<0三、解答題13．已知橢圓SKIPIF1<0的左焦點(diǎn)SKIPIF1<0，右頂點(diǎn)SKIPIF1<0．(1)求SKIPIF1<0的方程SKIPIF1<0(2)設(shè)SKIPIF1<0為SKIPIF1<0上一點(diǎn)（異于左、右頂點(diǎn)），SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，直線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0，求證：SKIPIF1<0．14．已知動點(diǎn)SKIPIF1<0與平面上點(diǎn)SKIPIF1<0，SKIPIF1<0的距離之和等于SKIPIF1<0.(1)求動點(diǎn)SKIPIF1<0的軌跡SKIPIF1<0方程；(2)若經(jīng)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與曲線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且點(diǎn)SKIPIF1<0為SKIPIF1<0的中點(diǎn)，求直線SKIPIF1<0的方程.15．已知橢圓SKIPIF1<0：SKIPIF1<0，焦點(diǎn)為SKIPIF1<0?SKIPIF1<0，過x軸上的一點(diǎn)M（m，0）（SKIPIF1