新高考數(shù)學(xué)二輪復(fù)習(xí) 模塊七 圓錐曲線（測試）（原卷版）

模塊七圓錐曲線（測試）（考試時間：120分鐘試卷滿分：150分）第Ⅰ卷一、選擇題：本題共8小題，每小題5分，共40分。在每小題給出的四個選項中，只有一項是符合題目要求的。1．已知直線SKIPIF1<0是雙曲線SKIPIF1<0的一條漸近線，則該雙曲線的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若拋物線SKIPIF1<0上一點(diǎn)SKIPIF1<0到焦點(diǎn)的距離為1，則點(diǎn)SKIPIF1<0的橫坐標(biāo)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．23．若動點(diǎn)SKIPIF1<0在SKIPIF1<0上移動，則點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0連線的中點(diǎn)的軌跡方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知拋物線SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則直線SKIPIF1<0的斜率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0是橢圓SKIPIF1<0和雙曲線SKIPIF1<0的公共焦點(diǎn)，P是它們的一個公共點(diǎn)，且SKIPIF1<0，則雙曲線SKIPIF1<0的離心率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0是SKIPIF1<0：SKIPIF1<0上一點(diǎn)，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0：SKIPIF1<0的兩條切線，切點(diǎn)分別為A，B，則當(dāng)直線AB與SKIPIF1<0平行時，直線AB的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知雙曲線SKIPIF1<0的左右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，P為雙曲線在第一象限上的一點(diǎn)，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．14 D．158．橢圓SKIPIF1<0任意兩條相互垂直的切線的交點(diǎn)軌跡為圓：SKIPIF1<0，這個圓稱為橢圓的蒙日圓．在圓SKIPIF1<0上總存在點(diǎn)SKIPIF1<0，使得過點(diǎn)SKIPIF1<0能作橢圓SKIPIF1<0的兩條相互垂直的切線，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、選擇題：本題共4小題，每小題5分，共20分。在每小題給出的選項中，有多項符合題目要求。全部選對的得5分，部分選對的得2分，有選錯的得0分。9．已知雙曲線SKIPIF1<0的兩個焦點(diǎn)分別為SKIPIF1<0，且滿足條件SKIPIF1<0，可以解得雙曲線SKIPIF1<0的方程為SKIPIF1<0，則條件SKIPIF1<0可以是（

）A．實軸長為4 B．雙曲線SKIPIF1<0為等軸雙曲線C．離心率為SKIPIF1<0 D．漸近線方程為SKIPIF1<010．已知圓SKIPIF1<0，SKIPIF1<0，則（

）A．直線SKIPIF1<0的方程為SKIPIF1<0B．過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線有且僅有SKIPIF1<0條C．兩圓相交，且公共弦長為SKIPIF1<0D．圓SKIPIF1<0上到直線SKIPIF1<0的距離為SKIPIF1<0的點(diǎn)共有SKIPIF1<0個11．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，準(zhǔn)線與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線SKIPIF1<0與拋物線SKIPIF1<0交于兩個不同的點(diǎn)SKIPIF1<0，則下列說法正確的有（

）A．當(dāng)SKIPIF1<0時，SKIPIF1<0B．SKIPIF1<0C．若直線SKIPIF1<0的傾斜角分別為SKIPIF1<0，則SKIPIF1<0D．若點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸的對稱點(diǎn)為點(diǎn)SKIPIF1<0，則直線SKIPIF1<0必恒過定點(diǎn)12．雙曲線具有以下光學(xué)性質(zhì)：從雙曲線的一個焦點(diǎn)發(fā)出的光線，經(jīng)雙曲線反射后，反射光線的反向延長線經(jīng)過雙曲線的另一個焦點(diǎn)．由此可得，過雙曲線上任意一點(diǎn)的切線平分該點(diǎn)與兩焦點(diǎn)連線的夾角．已知SKIPIF1<0分別為雙曲線SKIPIF1<0的左，右焦點(diǎn)，過SKIPIF1<0右支上一點(diǎn)SKIPIF1<0作雙曲線的切線交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，交SKIPIF1<0軸于點(diǎn)SKIPIF1<0，則（

）A．平面上點(diǎn)SKIPIF1<0的最小值為SKIPIF1<0B．直線SKIPIF1<0的方程為SKIPIF1<0C．過點(diǎn)SKIPIF1<0作SKIPIF1<0，垂足為SKIPIF1<0，則SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）D．四邊形SKIPIF1<0面積的最小值為4第Ⅱ卷三、填空題：本題共4小題，每小題5分，共20分。13．已知圓SKIPIF1<0，過SKIPIF1<0作圓SKIPIF1<0的切線SKIPIF1<0，則直線SKIPIF1<0的傾斜角為．14．已知橢圓SKIPIF1<0的右頂點(diǎn)、上頂點(diǎn)分別為A，B，直線SKIPIF1<0與直線SKIPIF1<0相交于點(diǎn)D，且點(diǎn)D到x軸的距離為a，則C的離心率為.15．已知雙曲線SKIPIF1<0的左，右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過左焦點(diǎn)SKIPIF1<0作直線SKIPIF1<0與雙曲線交于A，B兩點(diǎn)（B在第一象限），若線段SKIPIF1<0的中垂線經(jīng)過點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0，則雙曲線的離心率為.16．已知雙曲線SKIPIF1<0：SKIPIF1<0的焦距為SKIPIF1<0，過雙曲線SKIPIF1<0上任意一點(diǎn)SKIPIF1<0作直線SKIPIF1<0，SKIPIF1<0分別平行于兩條漸近線，且與兩條漸近線分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0．若四邊形SKIPIF1<0的面積為SKIPIF1<0，則雙曲線SKIPIF1<0的方程為．四、解答題：本題共6小題，共70分。解答應(yīng)寫出文字說明、證明過程或演算步棸。17．（10分）已知點(diǎn)SKIPIF1<0,直線SKIPIF1<0及圓SKIPIF1<0．(1)若直線SKIPIF1<0與圓SKIPIF1<0相切,求SKIPIF1<0的值．(2)求過SKIPIF1<0點(diǎn)的圓SKIPIF1<0的切線方程．18．（12分）設(shè)橢圓SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，且其左焦點(diǎn)坐標(biāo)為SKIPIF1<0.(1)求橢圓的方程；(2)對角線互相垂直的四邊形SKIPIF1<0的四個頂點(diǎn)都在SKIPIF1<0上，且兩條對角線均過SKIPIF1<0的右焦點(diǎn)，求SKIPIF1<0的最小值.19．（12分）已知F是拋物線E：SKIPIF1<0的焦點(diǎn)，SKIPIF1<0是拋物線E上一點(diǎn)，SKIPIF1<0與點(diǎn)F不重合，點(diǎn)F關(guān)于點(diǎn)M的對稱點(diǎn)為P，且SKIPIF1<0．(1)求拋物線E的標(biāo)準(zhǔn)方程；(2)若過點(diǎn)SKIPIF1<0的直線與拋物線E交于A，B兩點(diǎn)，求SKIPIF1<0的最大值．20．（12分）在直角坐標(biāo)系SKIPIF1<0中，拋物線SKIPIF1<0與直線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)．(1)若SKIPIF1<0點(diǎn)的橫坐標(biāo)為4，求拋物線在SKIPIF1<0點(diǎn)處的切線方程；(2)探究SKIPIF1<0軸上是否存在點(diǎn)SKIPIF1<0，使得當(dāng)SKIPIF1<0變動時，總有SKIPIF1<0？若存在，求出SKIPIF1<0點(diǎn)坐標(biāo)；若不存在，請說明理由．21．（12分）已知雙曲線SKIPIF1<0：SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0的一條漸近線與直線SKIPIF1<0：SKIPIF1<0垂直.(1)求SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)點(diǎn)SKIPIF1<0為SKIPIF1<0上一動點(diǎn)，直線