新高考數(shù)學(xué)一輪復(fù)習(xí)第8章 第08講 直線(xiàn)與橢圓、雙曲線(xiàn)、拋物線(xiàn) 精練（學(xué)生版）

第08講直線(xiàn)與橢圓、雙曲線(xiàn)、拋物線(xiàn)(精練）A夯實(shí)基礎(chǔ)B能力提升C綜合素養(yǎng)A夯實(shí)基礎(chǔ)一、單選題1．直線(xiàn)SKIPIF1<0與拋物線(xiàn)SKIPIF1<0的位置關(guān)系為（）A．相交 B．相切 C．相離 D．不能確定2．已知拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線(xiàn)為l，“SKIPIF1<0”是“F到l的距離大于2”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件3．已知SKIPIF1<0為橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)，SKIPIF1<0為SKIPIF1<0上關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(chēng)的兩點(diǎn)，且SKIPIF1<0，則四邊形SKIPIF1<0的面積為（

）A．2 B．4 C．6 D．84．設(shè)SKIPIF1<0為拋物線(xiàn)SKIPIF1<0：SKIPIF1<0的焦點(diǎn)，過(guò)SKIPIF1<0且傾斜角為SKIPIF1<0的直線(xiàn)交于SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0在SKIPIF1<0軸上方，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．橢圓SKIPIF1<0上的點(diǎn)SKIPIF1<0到直線(xiàn)SKIPIF1<0：SKIPIF1<0的距離的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知橢圓SKIPIF1<0，則以點(diǎn)SKIPIF1<0為中點(diǎn)的弦所在的直線(xiàn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．過(guò)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)SKIPIF1<0且斜率為SKIPIF1<0的直線(xiàn)交拋物線(xiàn)SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，拋物線(xiàn)的準(zhǔn)線(xiàn)為SKIPIF1<0，SKIPIF1<0于SKIPIF1<0，SKIPIF1<0于SKIPIF1<0，則四邊形SKIPIF1<0的面積為（

）A．32 B．SKIPIF1<0 C．64 D．SKIPIF1<08．已知P為橢圓SKIPIF1<0上任意一點(diǎn)，EF為圓SKIPIF1<0任意一條直徑，則SKIPIF1<0的取值范圍為（

）A．[8，12] B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．已知雙曲線(xiàn)SKIPIF1<0，則下列說(shuō)法正確的（

）A．雙曲線(xiàn)C的離心率等于半焦距的長(zhǎng)B．雙曲線(xiàn)SKIPIF1<0與雙曲線(xiàn)C有相同的漸近線(xiàn)C．直線(xiàn)SKIPIF1<0被雙曲線(xiàn)C截得的弦長(zhǎng)為SKIPIF1<0D．直線(xiàn)SKIPIF1<0與雙曲線(xiàn)C的公共點(diǎn)個(gè)數(shù)只可能為0，1，210．橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則以下說(shuō)法正確的是（

）A．過(guò)點(diǎn)SKIPIF1<0的直線(xiàn)與橢圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的周長(zhǎng)為8B．橢圓SKIPIF1<0上不存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0C．直線(xiàn)SKIPIF1<0與橢圓SKIPIF1<0恒有公共點(diǎn)D．SKIPIF1<0為橢圓SKIPIF1<0上一點(diǎn)，SKIPIF1<0為圓SKIPIF1<0上一點(diǎn)，則點(diǎn)SKIPIF1<0，SKIPIF1<0的最大距離為3三、填空題11．設(shè)SKIPIF1<0是橢圓SKIPIF1<0左，右焦點(diǎn)，P為直線(xiàn)SKIPIF1<0上一點(diǎn)，若SKIPIF1<0是底角為SKIPIF1<0的等腰三角形，則橢圓SKIPIF1<0的離心率為_(kāi)__．12．直線(xiàn)SKIPIF1<0與拋物線(xiàn)SKIPIF1<0交于A(yíng)，B兩點(diǎn)，設(shè)拋物線(xiàn)C的焦點(diǎn)是F，若SKIPIF1<0，則SKIPIF1<0________．四、解答題13．已知橢圓SKIPIF1<0過(guò)橢圓右焦點(diǎn)SKIPIF1<0，且垂直于SKIPIF1<0軸的直線(xiàn)與橢圓在第一象限交于點(diǎn)SKIPIF1<0，已知橢圓的左焦點(diǎn)為SKIPIF1<0，SKIPIF1<0的面積是SKIPIF1<0．(1)求橢圓的標(biāo)準(zhǔn)方程；(2)設(shè)直線(xiàn)SKIPIF1<0與橢圓交與SKIPIF1<0、SKIPIF1<0兩點(diǎn)，當(dāng)SKIPIF1<0時(shí)，求直線(xiàn)SKIPIF1<0的方程．14．已知拋物線(xiàn)SKIPIF1<0上的點(diǎn)SKIPIF1<0到焦點(diǎn)SKIPIF1<0的距離為SKIPIF1<0．(1)求拋物線(xiàn)SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)直線(xiàn)SKIPIF1<0與拋物線(xiàn)SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩個(gè)不同的點(diǎn)，若SKIPIF1<0，求直線(xiàn)SKIPIF1<0的方程．B能力提升1．過(guò)拋物線(xiàn)SKIPIF1<0的焦點(diǎn)SKIPIF1<0作傾斜角為SKIPIF1<0的直線(xiàn)SKIPIF1<0交SKIPIF1<0于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，以?huà)佄锞€(xiàn)SKIPIF1<0的準(zhǔn)線(xiàn)SKIPIF1<0上一點(diǎn)SKIPIF1<0為圓心作圓SKIPIF1<0經(jīng)過(guò)SKIPIF1<0、SKIPIF1<0兩點(diǎn)，則圓SKIPIF1<0的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線(xiàn)為l，且l過(guò)點(diǎn)SKIPIF1<0，M在拋物線(xiàn)C上，若點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．4 B．5 C．6 D．73．已知點(diǎn)A在雙曲線(xiàn)C：SKIPIF1<0（b>0）上，且雙曲線(xiàn)C的上?下焦點(diǎn)分別為F1，F(xiàn)2，點(diǎn)B在∠F1AF2的平分線(xiàn)上，BF2⊥AB，若點(diǎn)D在直線(xiàn)l：SKIPIF1<0，則|BD|的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知橢圓SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0?SKIPIF1<0，過(guò)SKIPIF1<0且斜率為SKIPIF1<0的直線(xiàn)與橢圓交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0為鈍角，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0C綜合素養(yǎng)1．已知雙曲線(xiàn)SKIPIF1<0與橢圓SKIPIF1<0有公共焦點(diǎn)，且它的一條漸近線(xiàn)為SKIPIF1<0.(1)求雙曲線(xiàn)SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)拋物線(xiàn)SKIPIF1<0的準(zhǔn)線(xiàn)過(guò)雙曲線(xiàn)SKIPIF1<0的左頂點(diǎn)，斜率為1的直線(xiàn)SKIPIF1<0過(guò)雙曲線(xiàn)SKIPIF1<0的右頂點(diǎn)且交拋物線(xiàn)SKIPIF1<0于SKIPIF1<0兩點(diǎn)，求SKIPIF1<0.2．已知拋物線(xiàn)SKIPIF1<0的焦點(diǎn)為F，過(guò)F的直線(xiàn)與拋物線(xiàn)C交于A(yíng)，B兩點(diǎn)，當(dāng)A，B兩點(diǎn)的縱坐標(biāo)相同時(shí)，SKIPIF1<0．(1)求拋物線(xiàn)C的方程；(2)若P，Q為拋物線(xiàn)C上兩個(gè)