中考精品：数学压轴题汇编(含解题过程,共67页).pdf

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1、⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯最新资料推荐⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯冲刺中考数学压轴题汇编(含解题过程)（2009年重庆市）26．已知：如图，在平面直角坐标系xOy中，矩形OABC的边OA在y轴的正半轴上，OC在x轴的正半轴上，OA=2，OC=3．过原点O作∠AOC的平分线交AB于点D，连接DC，过点D作DE⊥DC，交OA于点E．（1）求过点E、D、C的抛物线的解析式；（2）将∠EDC绕点D按顺时针方向旋转后，角的一边与y轴的正半轴交于点F，另一边与6线段OC交于点G．如果DF与（1）中的抛物线交于另一点M，点M的横坐标为，那么5EF=2GO是否成立

2、？若成立，请给予证明；若不成立，请说明理由；（3）对于（2）中的点G，在位于第一象限内的该抛物线上是否存在点Q，使得直线GQ与AB的交点P与点C、G构成的△PCG是等腰三角形？若存在，请求出点Q的坐标；若不存在，请说明理由．yDABExOC26题图26．解：（1）由已知，得C(3，0)，D(2，2)，ADE90°CDBBCD，1AEADtanADE2tanBCD21．2E(0，1)．····························································································（1分）2设过

3、点E、D、C的抛物线的解析式为yaxbxc(a0)．将点E的坐标代入，得c1．将c1和点D、C的坐标分别代入，得4a2b12，······················································································（2分）9a3b10.5a6解这个方程组，得13b65213故抛物线的解析式为yxx1．···················································（3分）661⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯最新资料推荐⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

4、⋯⋯⋯⋯⋯⋯⋯（2）EF2GO成立．···········································································（4分）6点M在该抛物线上，且它的横坐标为，512点M的纵坐标为．···········································································（5分）5yF设DM的解析式为ykxb1(k0)，ＭD将点D、M的坐标分别代入，得AB2kb12，1Ek，612解得2kb1.55b13．xOGKC1DM的解析式为yx3．·····

5、·························································（6分）2F(0，3)，EF2．·············································································（7分）过点D作DK⊥OC于点K，则DADK．ADKFDG90°，FDAGDK．又FADGKD90°，△DAF≌△DKG．KGAF1．GO1．·······································································

6、·····················（8分）EF2GO．（3）点P在AB上，G(1，0)，C(3，0)，则设P(1，2)．222222PG(t1)2，PC(3t)2，GC2．2222①若PGPC，则(t1)2(3t)2，解得t2．P(2，2)，此时点Q与点P重合．Q(2，2)．···························································································（9分）22②若PGGC，则(t1)22，解得t1，P(1，2)，此时GP⊥x轴．GP与该抛物线在第一象限内的交点Q的

7、横坐标为1，7点Q的纵坐标为．32⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯最新资料推荐⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯7Q1，．························································································（10分）3222③若PCGC，则(3t)22，解得t3，P(3，2)，此时PCGC2，△PCG是等腰直角三角形．过点Q作QH⊥x轴于点H，y则QHGH，设QHh，Q(Q)D(P)