2026版《优化设计大一轮》高考数学（优化设计新高考版）课时规范练55直线与圆锥曲线的位置关系

课时规范练55直线与圆锥曲线的位置关系高考总复习优化设计GAOKAOZONGFUXIYOUHUASHEJI2026基础巩固练12345678910111213141516

B

123456789101112131415162.直线x+y+2=0与抛物线C:y2=ax(a≠0)的图象相切,则C的准线方程为(

)A.x=-2 B.x=-1C.y=-2 D.y=-1A

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C

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123456789101112131415169.(2024·江西宜春三模)已知抛物线C:y2=4x的焦点为F,动直线l与抛物线C交于异于原点O的A,B两点,以线段OA,OB为邻边作平行四边形OAPB,若点P(4,m)(m>0),则当|AB|取最大值时,m的值为

.

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综合提升练A12345678910111213141516

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D

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12345678910111213141516(方法二)设线段F1M的垂直平分线l与C恰有一个公共点为P,则当点P不在长轴时,线段F1M的垂直平分线l即为点P处C的切线,也为∠F1PM的角平分线,作∠F1PF2的角平分线PH,根据椭圆的性质易知PH⊥l,所以∠F1PE+∠F1PH=90°,则∠F2PH+∠EPM=90°,故∠F2PF1+∠F1PM=180°,所以M,P,F2三点共线,所以|MF2|=|MP|+|PF2|=|PF1|+|PF2|=4,所以点M的轨迹是以F2为圆心,4为半径的圆,当P在椭圆长轴上时,点M为(5,0)或(-3,0),也满足|MF2|=4,故点M的轨迹是圆,该圆的方程为(x-1)2+y2=16.12345678910111213141516