发布时间 : 星期三 文章中考数学压轴题100题精选(91-100题)答案更新完毕开始阅读27a9d365a7e9856a561252d380eb6294dd882289
∠DAP=∠CAO, ∴△ADP∽△AOC. ∴
DPCODP432,即. ??.∴DP?DACA8551024253471. ??25410∴DE?DP2?PE2?∴S四边形DEPF=34713471,即S=. ·············································································· 14分 44(注:本卷中所有题目,若由其它方法得出正确结论,请参照标准给分.)
【094】解:(1)令二次函数y?ax?bx?c,则
2?16a?4b?c?0? ························································································································ 1分 ?a?b?c?0?c?2?1?a???2?3?·································································································································· 2分 ??b?? ·2??c?2??13?过A,B,C三点的抛物线的解析式为y??x2?x?2 ············································· 4分
220? (2)以AB为直径的圆圆心坐标为O??,?3?2??53 O?O? ··············································································································· 5分 22·························································································· 6分 QCD为圆O?切线 ?OC??CD ·
??O?CD??DCO?90°
?CO?O??O?CO?90° ??CO?O??DCO
······································································ 8分 ?△O?CO∽△CDO O?O/OC?OC/OD ·
38/2?2/OD ?OD? 23?O?C??8?····················································································································· 9分 ?D坐标为?0,? ·
?3?(3)存在 ···································································································································· 10分 抛物线对称轴为X??3 233?r,r)或F(??r,r) 22设满足条件的圆的半径为r,则E的坐标为(?而E点在抛物线y??123x?x?2上 221333?r??(??r)2?(??r)?2
2222?r1??1?2929 r2??1? 222929,1? ············ 12分 22故在以EF为直径的圆,恰好与x轴相切,该圆的半径为?1?注:解答题只要方法合理均可酌情给分
【095】(1)B(4,0),C(0,····················································································· 2分 ?2). ·
123·················································································································· 4分 x?x?2. ·
22(2)△ABC是直角三角形. ··································································································· 5分
123证明:令y?0,则x?x?2?0.
22y??x1??1,x2?4.
································································································································ 6分 ?A(?1,0). ·解法一:?AB?5,AC?5,BC?25. ······································································· 7分
?AC2?BC2?5?20?25?AB2.
········································································································· 8分 ?△ABC是直角三角形. ·
COAO1解法二:QAO?1,CO?2,BO?4,???
BOOC2Q?AOC??COB?90°,
·············································································································· 7分 ?△AOC∽△COB. ·
??ACO??CBO.
Q?CBO??BCO?90°,
??ACO??BCO?90°.即?ACB?90°.
········································································································· 8分 ?△ABC是直角三角形. ·
(3)能.①当矩形两个顶点在AB上时,如图1,CO交GF于H.
QGF∥AB,
?△CGF∽△CAB. GFCH??. ······························································· 9分 ABCO2解法一:设GF?x,则DE?x,CH?x,
52DG?OH?OC?CH?2?x.
52?2??S矩形DEFG?x·?2?x???x2?2x
5?5?y D A E O B x F G H C 图1
2?5?5=??x???. ················································································································· 10分
5?2?25时,S最大. 25?DE?,DG?1.
2Q△ADG∽△AOC, ADDG11??,?AD?,?OD?,OE?2. AOOC22当x?2?1??D??,0?,E(2,········································································································ 11分 0). ·
?2?10?5x. 210?5x555················································ 10分 ?S矩形DEFG?x·??x2?5x??(x?1)2?.·
2222?当x?1时,S最大.
5?DG?1,DE?.
2Q△ADG∽△AOC, ADDG11??,?AD?,?OD?,OE?2. AOOC22解法二:设DG?x,则DE?GF??1??D??,0?,E(2,········································································································ 11分 0). ·
?2?y ②当矩形一个顶点在AB上时,F与C重合,如图2,
QDG∥BC, ?△AGD∽△ACB. GDAG. ??BCAF解法一:设GD?x,?AC?5,BC?25,
D O A G C 图2
B G x x?GF?AC?AG?5?.
2x?1?·?5????x2?5x ?S矩形DEFG?x2?2?1x?5=?2??25?. ··············································································································· 12分 2当x?5时,S最大.
?GD?5,AG?55322,?AD?AG?GD?.?OD? 222?3??D?,0? ································································································································· 13分
2??解法二:设DE?x,QAC?5,BC?25,?GC?x,AG?5?x.?GD?25?2x.
?S矩形DEFG?x·25?2x??2x2?25x
?5?5=?2?x?·················································································································· 12分 ????2 ·2???当x?2??5时,S最大, 255322.?AD?AG?GD?.?OD?. 222?GD?5,AG??3?0? ·?D?,································································································································ 13分 ?2?0?,综上所述:当矩形两个顶点在AB上时,坐标分别为??,(2,0);
?3?2???1?2??0? ·当矩形一个顶点在AB上时,坐标为?,········································································· 14分
【096】(1)因所求抛物线的顶点M的坐标为(2,4),
故可设其关系式为y?a?x?2??4 ………………(1分) 又抛物线经过O(0,0),于是得a?0?2??4?0, ………………(2分) 解得 a=-1 ………………(3分) ∴ 所求函数关系式为y???x?2??4,即y??x?4x. ……………(4分)
2222(2)① 点P不在直线ME上. ………………(5分)
根据抛物线的对称性可知E点的坐标为(4,0), 又M的坐标为(2,4),设直线ME的关系式为y=kx+b.
?4k?b?0?k??2于是得? ,解得?
?2k?b?4?b?8所以直线ME的关系式为y=-2x+8. ……(6分)
5555?由已知条件易得,当t?时,OA=AP?,?P??,? ……………(7分)
22?22?∵ P点的坐标不满足直线ME的关系式y=-2x+8.
5∴ 当t?时,点P不在直线ME上. ………………(8分)
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