新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第29練 拋物線（原卷版）

第29練拋物線學(xué)校____________姓名____________班級____________一、單選題1．拋物線SKIPIF1<0的焦點到其準(zhǔn)線的距離是（

）A．1 B．2 C．3 D．42．已知拋物線SKIPIF1<0：SKIPIF1<0的焦點為SKIPIF1<0，點SKIPIF1<0在拋物線上，SKIPIF1<0，則點SKIPIF1<0的橫坐標(biāo)為（

）A．6 B．5 C．4 D．23．過點SKIPIF1<0，且焦點在y軸上的拋物線的標(biāo)準(zhǔn)方程是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．拋物線SKIPIF1<0上A點到焦點F的距離為SKIPIF1<0，則點A的縱坐標(biāo)為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知拋物線SKIPIF1<0的焦點為F，準(zhǔn)線為l，點P在C上，直線PF交y軸于點Q，若SKIPIF1<0，則點P到準(zhǔn)線l的距離為（

）A．3 B．4 C．5 D．66．已知拋物線E:SKIPIF1<0的準(zhǔn)線交y軸于點M，過點M作直線l交E于A，B兩點，且SKIPIF1<0，則直線l的斜率是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知O是坐標(biāo)原點，F(xiàn)是拋物線C：SKIPIF1<0的焦點，SKIPIF1<0是C上一點，且SKIPIF1<0，則SKIPIF1<0的面積為（

）A．8 B．6 C．4 D．28．已知拋物線SKIPIF1<0焦點的坐標(biāo)為SKIPIF1<0，P為拋物線上的任意一點，SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．3 B．4 C．5 D．SKIPIF1<09．已知拋物線SKIPIF1<0，點SKIPIF1<0，SKIPIF1<0是曲線W上兩點，若SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．10 B．14 C．12 D．1610．在平面直角坐標(biāo)系SKIPIF1<0中，拋物線SKIPIF1<0的焦點為SKIPIF1<0是SKIPIF1<0上位于第一象限內(nèi)的一點，若SKIPIF1<0在點SKIPIF1<0處的切線與SKIPIF1<0軸交于SKIPIF1<0點，與SKIPIF1<0軸交于SKIPIF1<0點，則與SKIPIF1<0相等的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題11．已知拋物線C：SKIPIF1<0的焦點為F，P為拋物線上一點，則下列結(jié)論正確的有（

）A．焦點F到拋物線準(zhǔn)線的距離為2B．若SKIPIF1<0，則點P的坐標(biāo)為SKIPIF1<0C．過焦點F且垂直于x軸的直線被拋物線所截得的弦長為2D．若點M的坐標(biāo)為SKIPIF1<0，則SKIPIF1<0的最小值為412．已知拋物線SKIPIF1<0的焦點為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是拋物線上兩點，則下列結(jié)論正確的是（

）A．點SKIPIF1<0的坐標(biāo)為SKIPIF1<0B．若直線SKIPIF1<0過點SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<0D．若SKIPIF1<0，則線段SKIPIF1<0的中點SKIPIF1<0到SKIPIF1<0軸的距離為SKIPIF1<0三、解答題13．已知拋物線SKIPIF1<0的焦點為SKIPIF1<0，直線SKIPIF1<0與拋物線SKIPIF1<0交于SKIPIF1<0兩點，當(dāng)SKIPIF1<0時，SKIPIF1<0為坐標(biāo)原點）是等邊三角形.(1)求拋物線SKIPIF1<0的方程.(2)延長SKIPIF1<0交拋物線SKIPIF1<0于點SKIPIF1<0，試問直線SKIPIF1<0是否恒過點SKIPIF1<0？若是，求出點SKIPIF1<0的坐標(biāo)；若不是，請說明理由.14．已知P(1，2)在拋物線C：y2＝2px上．(1)求拋物線C的方程；(2)A，B是拋物線C上的兩個動點，如果直線PA的斜率與直線PB的斜率之和為2，證明：直線AB過定點．15．已知拋物線SKIPIF1<0上的點SKIPIF1<0與焦點SKIPIF1<0的距離為SKIPIF1<0，且點SKIPIF1<0的縱坐標(biāo)為SKIPIF1<0.(1)求拋物線SKIPIF1<0