新高考數(shù)學(xué)二輪復(fù)習(xí)圓錐曲線專題突破提升練習(xí)第1講 圓錐曲線第一定義與焦點(diǎn)三角形（原卷版）

第1講圓錐曲線第一定義與焦點(diǎn)三角形一．選擇題（共8小題）1．已知橢圓SKIPIF1<0的焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線與橢圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的方程為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若橢圓SKIPIF1<0和雙曲線SKIPIF1<0有相同的焦點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是兩條曲線的一個(gè)交點(diǎn)，則SKIPIF1<0的值是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，SKIPIF1<0是雙曲線右支上一點(diǎn)，SKIPIF1<0，△SKIPIF1<0的面積為SKIPIF1<0，則雙曲線的離心率為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知SKIPIF1<0，SKIPIF1<0分別是雙曲線SKIPIF1<0的左、右焦點(diǎn)，以SKIPIF1<0為直徑的圓與此雙曲線在第一象限內(nèi)的交點(diǎn)為SKIPIF1<0，且SKIPIF1<0，則此雙曲線的離心率是SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．2 C．4 D．55．在平面直角坐標(biāo)系SKIPIF1<0中，雙曲線的SKIPIF1<0右支與焦點(diǎn)為SKIPIF1<0的拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則該雙曲線的漸近線方程為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知雙曲線SKIPIF1<0的右支與焦點(diǎn)為SKIPIF1<0的拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則雙曲線SKIPIF1<0的漸近線方程為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．將兩個(gè)頂點(diǎn)在拋物線SKIPIF1<0上，另一個(gè)頂點(diǎn)是此拋物線焦點(diǎn)的正三角形個(gè)數(shù)記為SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．在平面直角坐標(biāo)系SKIPIF1<0中，雙曲線SKIPIF1<0的右支與焦點(diǎn)為SKIPIF1<0的拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，已知雙曲線SKIPIF1<0的一條漸近線方程為SKIPIF1<0，且SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．4二．多選題（共2小題）9．過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0作直線交拋物線于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0為SKIPIF1<0的中點(diǎn)，則SKIPIF1<0SKIPIF1<0A．以線段SKIPIF1<0為直徑的圓與SKIPIF1<0軸相切 B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 C．以線段SKIPIF1<0為直徑的圓與直線SKIPIF1<0相離 D．SKIPIF1<0的最小值為310．已知拋物線SKIPIF1<0，過焦點(diǎn)SKIPIF1<0的直線交拋物線SKIPIF1<0于SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0兩點(diǎn)，直線SKIPIF1<0，SKIPIF1<0分別于直線SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．則下列說法正確的是SKIPIF1<0SKIPIF1<0A．焦點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0的最小值為4 D．SKIPIF1<0與SKIPIF1<0的面積之比為定值三．填空題（共7小題）11．已知橢圓SKIPIF1<0的兩個(gè)焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0的直線與橢圓SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的方程為．12．已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為橢圓上一點(diǎn)，且滿足SKIPIF1<0為坐標(biāo)原點(diǎn)）．若SKIPIF1<0，則橢圓的離心率為．13．已知橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，過SKIPIF1<0的通徑SKIPIF1<0（過焦點(diǎn)垂直于長(zhǎng)軸的弦叫做通徑），則SKIPIF1<0的內(nèi)切圓方程為．14．過拋物線SKIPIF1<0的焦點(diǎn)作斜率為1的直線與該拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0軸上的正射影分別為SKIPIF1<0，SKIPIF1<0．若梯形SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0．15．過拋物線SKIPIF1<0的焦點(diǎn)作斜率為SKIPIF1<0的直線與該拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0軸上的正射影分別為SKIPIF1<0，SKIPIF1<0，若梯形SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0．16．過拋物線SKIPIF1<0的焦點(diǎn)作斜率為1的直線與該拋物線交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，又過SKIPIF1<0，SKIPIF1<0兩點(diǎn)作SKIPIF1<0軸的垂線，垂足分別為SKIPIF1<0，SKIPIF1<0，若梯形SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<017．在平面直角坐標(biāo)系SKIPIF1<0中，雙曲線SKIPIF1<0．SKIPIF1<0的右支與焦點(diǎn)為SKIPIF1<0的拋物線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，已知雙曲線的離心率為SKIPIF1<0，若SKIPIF1<0．則SKIPIF1<0．四．解答題（共1小題）18．已知橢圓SKIPIF1<0過點(diǎn)SKIPIF1<0，SKIPIF1<0，橢圓SKIPIF1<0與SKIPIF1<0軸交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，與SKIPIF1<0軸交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．（1