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20 拋物線中向量問題(原卷版)

專題20拋物線中向量問題限時(shí)：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SKIPIF1<0的頂點(diǎn)都在拋物線SKIPIF1<0上，且SKIPIF1<0的重心為拋物線的焦點(diǎn)F，則SKIPIF1<0（

）A．3 B．6 C．9 D．122．拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線交拋物線于SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0為平面上任意一點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．53．已知直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，與圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0在SKIPIF1<0軸的同側(cè)，則SKIPIF1<0（

）A．1 B．2 C．3 D．44．已知拋物線SKIPIF1<0的焦點(diǎn)為F，C的準(zhǔn)線與對(duì)稱軸交于D，過D的直線l與C交于A，B兩點(diǎn)，且SKIPIF1<0，若FB為SKIPIF1<0的平分線，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．8 C．10 D．SKIPIF1<05．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，動(dòng)點(diǎn)SKIPIF1<0在SKIPIF1<0上，圓SKIPIF1<0的半徑為1，過點(diǎn)SKIPIF1<0的直線與圓SKIPIF1<0相切于點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．2 B．3 C．4 D．56．在平面直角坐標(biāo)系SKIPIF1<0中，若拋物線SKIPIF1<0的準(zhǔn)線與圓SKIPIF1<0相切于點(diǎn)SKIPIF1<0，直線SKIPIF1<0與拋物線SKIPIF1<0切于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知過拋物線SKIPIF1<0的焦點(diǎn)F的直線l交拋物線于A，B兩點(diǎn)，若D為線段AB的中點(diǎn)，連接OD并延長(zhǎng)交拋物線C于點(diǎn)M，若SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．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．2二、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．設(shè)F為拋物線C：SKIPIF1<0的焦點(diǎn)，過F且傾斜角為30°的直線交C于A，B兩點(diǎn)，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．已知拋物線C的方程為SKIPIF1<0，過C焦點(diǎn)F的直線與C交于M，N兩點(diǎn)，直線MO與C的準(zhǔn)線交于Q點(diǎn)（其中O為坐標(biāo)原點(diǎn)），P為C準(zhǔn)線上的一個(gè)動(dòng)點(diǎn)，下列選項(xiàng)正確的是（

）A．當(dāng)直線MN垂直x軸時(shí)，弦MN的長(zhǎng)度最短B．SKIPIF1<0為定值SKIPIF1<0C．當(dāng)PM與C的準(zhǔn)線垂直時(shí)，必有SKIPIF1<0D．至少存在兩個(gè)點(diǎn)P，使得SKIPIF1<0

11．已知點(diǎn)A是拋物線SKIPIF1<0上的動(dòng)點(diǎn)，SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0為焦點(diǎn)，SKIPIF1<0，且SKIPIF1<0三點(diǎn)順時(shí)針排列，則（

）A．當(dāng)點(diǎn)SKIPIF1<0在SKIPIF1<0軸上時(shí)，SKIPIF1<0B．當(dāng)點(diǎn)SKIPIF1<0在SKIPIF1<0軸上時(shí)，點(diǎn)A的坐標(biāo)為SKIPIF1<0C．當(dāng)點(diǎn)A與點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸對(duì)稱時(shí)，SKIPIF1<0D．若SKIPIF1<0，則點(diǎn)A與點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸對(duì)稱12．拋物線的弦與過弦的端點(diǎn)的兩條切線所圍成的三角形稱為阿基米德三角形.設(shè)拋物線SKIPIF1<0，弦SKIPIF1<0過焦點(diǎn)SKIPIF1<0為其阿基米德三角形，則下列結(jié)論一定成立的是（

）A．存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0B．SKIPIF1<0C．對(duì)于任意的點(diǎn)SKIPIF1<0，必有向量SKIPIF1<0與向量SKIPIF1<0共線D．SKIPIF1<0面積的最小值為SKIPIF1<0三、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．已知拋物線SKIPIF1<0的焦點(diǎn)為F，過F的直線SKIPIF1<0與拋物線交于A，B兩點(diǎn)，且SKIPIF1<0，O為坐標(biāo)原點(diǎn)，則SKIPIF1<0的面積為.14．已知F是拋物線SKIPIF1<0的焦點(diǎn)，M是C上一點(diǎn)，F(xiàn)M的延長(zhǎng)線交y軸于點(diǎn)N，若SKIPIF1<0，則SKIPIF1<015．已知拋物線C：SKIPIF1<0的焦點(diǎn)為F，準(zhǔn)線為SKIPIF1<0，經(jīng)過點(diǎn)F的直線與拋物線C相交A，B兩點(diǎn)，SKIPIF1<0與x軸相交于點(diǎn)M，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0.16．已知拋物線SKIPIF1<0與圓SKIPIF1<0，過拋物線的焦點(diǎn)SKIPIF1<0作斜率為SKIPIF1<0的直線SKIPIF1<0與拋物線交于SKIPIF1<0兩點(diǎn)，與圓交于SKIPIF1<0兩點(diǎn)（SKIPIF1<0在SKIPIF1<0軸的同一側(cè)），若SKIPIF1<0，則SKIPIF1<0的值是．四、解答題：本大題共6小題，共70分.解答應(yīng)寫出必要的文字說明、證明過程或演算步驟．17．已知SKIPIF1<0是拋物線SKIPIF1<0上一點(diǎn)，且M到C的焦點(diǎn)的距離為5.

(1)求拋物線C的方程及點(diǎn)M的坐標(biāo)；(2)如圖所示，過點(diǎn)SKIPIF1<0的直線l與C交于A，B兩點(diǎn)，與y軸交于點(diǎn)Q，設(shè)SKIPIF1<0，SKIPIF1<0，求證：SKIPIF1<0是定值.18．已知SKIPIF1<0，SKIPIF1<0為橢圓C的左右焦點(diǎn)，且拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，M為橢圓的上頂點(diǎn)，SKIPIF1<0的面積為SKIPIF1<0.(1)求橢圓C的標(biāo)準(zhǔn)方程；(2)過點(diǎn)SKIPIF1<0的直線l與橢圓C交于A，B兩點(diǎn)，О為坐標(biāo)原點(diǎn)，且SKIPIF1<0，若橢圓C上存在一點(diǎn)E，使得四邊形OAED為平行四邊形，求SKIPIF1<0的取值范圍.19．已知橢圓SKIPIF1<0：SKIPIF1<0的離心率為SKIPIF1<0，且其中一個(gè)焦點(diǎn)與拋物線SKIPIF1<0的焦點(diǎn)重合．(1)求橢圓SKIPIF1<0的方程；(2)若直線SKIPIF1<0：SKIPIF1<0與橢圓SKIPIF1<0交于不同的A，B兩點(diǎn)，且滿足SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)），求弦長(zhǎng)SKIPIF1<0的值．20．已知拋物線SKIPIF1<0，點(diǎn)SKIPIF1<0在拋物線上，直線SKIPIF1<0交SKIPIF1<0于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0是線段SKIPIF1<0的中點(diǎn)，過SKIPIF1<0作SKIPIF1<0軸的垂線交SKIPIF1<0于點(diǎn)SKIPIF1<0．(1)求點(diǎn)SKIPIF1<0到拋物線焦點(diǎn)的距離；(2)是否存在實(shí)數(shù)SKIPIF1<0使SKIPIF1<0，若存在，求SKIPIF1<0的值；若不存在，說明理由．21．已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0