单元形成性评价(三).pptx

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1、1单元形成性评价单元形成性评价(三)(第三章)(120分钟150分)212345678910111213141516171819202122一、单选题(每小题5分,共40分)1.“m3”是“曲线mx2-(m-2)y2=1为双曲线”的()A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件3123456789101112131415161718192021224123456789101112131415161718192021225123456789101112131415161718192021223.已知抛物线y2=2px(p0)的准线经过点(-1,1),则抛物线的焦点坐

2、标为()A.(-1,0)B.(1,0)C.(0,-1)D.(0,1)61234567891011121314151617181920212271234567891011121314151617181920212281234567891011121314151617181920212291234567891011121314151617181920212210123456789101112131415161718192021221112345678910111213141516171819202122121234567891011121314151617181920212213123456789

3、10111213141516171819202122141234567891011121314151617181920212210.若ab0,则方程ax-y+b=0和bx2+ay2=ab在同一坐标系中所表示的图象不可能是下图中的()1512345678910111213141516171819202122161234567891011121314151617181920212217123456789101112131415161718192021221812345678910111213141516171819202122191234567891011121314151617181920212

4、220123456789101112131415161718192021222112345678910111213141516171819202122221234567891011121314151617181920212223123456789101112131415161718192021222412345678910111213141516171819202122251234567891011121314151617181920212226123456789101112131415161718192021222712345678910111213141516171819202122281

5、234567891011121314151617181920212219.(12分)已知抛物线C:y2=2px(p0)的焦点为F(1,0),抛物线E:x2=2py的焦点为M,O为坐标原点.(1)若过点M的直线l与抛物线C有且只有一个交点,求直线l的方程;(2)若直线MF与抛物线C交于A,B两点,求OAB的面积.【解析】(1)因为抛物线C:y2=2px(p0)的焦点为F(1,0),抛物线E:x2=2py的焦点为M,所以p=2,M(0,1).当直线l的斜率不存在时,其方程为x=0,满足题意.当直线l的斜率存在时,设方程为y=kx+1,代入y2=4x,得k2x2+(2k-4)x+1=0.291234

6、56789101112131415161718192021223012345678910111213141516171819202122311234567891011121314151617181920212220.(12分)已知点A(x1,y1),B(x2,y2)是抛物线C:x2=4y上的两点,满足OAOB,O是坐标原点.(1)求证:x1x2=-16;(2)若ODAB于点D,求点D的轨迹方程.3212345678910111213141516171819202122即x1x2+(kx1+b)(kx2+b)=(1+k2)x1x2+bk(x1+x2)+b2=0,可得-4(1+k2)b+4k2b+

7、b2=0,b0,解得b=4.此时=16k2+16b0成立,所以x1x2=-4b=-16.(2)由(1)可得直线AB的方程为y=kx+4,所以直线AB过定点M(0,4),又ODAB于点D,所以点D在以OM为直径的圆上,所以点D的轨迹方程为x2+(y-2)2=4.3312345678910111213141516171819202122341234567891011121314151617181920212235123456789101112131415161718192021223612345678910111213141516171819202122371234567891011121314151617181920212238123456789101112131415161718192021223912345678910111213141516171819202122本课结束