广西钦州市

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26．解：（1）（0，－3），b＝－

9，c＝－3． ··················································· 3分 439（2）由（1），得y＝x2－x－3，它与x轴交于A，B两点，得B（4，0）．

44y ∴OB＝4，又∵OC＝3，∴BC＝5．

QH由题意，得△BHP∽△BOC，

AOBx∵OC∶OB∶BC＝3∶4∶5， P∴HP∶HB∶BP＝3∶4∶5， ∵PB＝5t，∴HB＝4t，HP＝3t． C∴OH＝OB－HB＝4－4t．

3由y＝x－3与x轴交于点Q，得Q（4t，0）．

4t∴OQ＝4t． ·············································································· 4分 ①当H在Q、B之间时， QH＝OH－OQ

＝（4－4t）－4t＝4－8t． ······················································· 5分 ②当H在O、Q之间时， QH＝OQ－OH

＝4t－（4－4t）＝8t－4． ······················································· 6分综合①，②得QH＝｜4－8t｜； ······················································ 6分（3）存在t的值，使以P、H、Q为顶点的三角形与△COQ相似． ················ 7分

①当H在Q、B之间时，QH＝4－8t，

4?8t3t若△QHP∽△COQ，则QH∶CO＝HP∶OQ，得＝，

34t7∴t＝． ··············································································· 7分

323t4?8t若△PHQ∽△COQ，则PH∶CO＝HQ∶OQ，得＝，

4t3即t2＋2t－1＝0．

∴t1＝2－1，t2＝－2－1（舍去）． ········································· 8分 ②当H在O、Q之间时，QH＝8t－4．

8t?43t若△QHP∽△COQ，则QH∶CO＝HP∶OQ，得＝，

34t25∴t＝． ··············································································· 9分

323t8t?4若△PHQ∽△COQ，则PH∶CO＝HQ∶OQ，得＝，

4t3即t2－2t＋1＝0．

∴t1＝t2＝1（舍去）． ······························································ 10分

725综上所述，存在t的值，t1＝2－1，t2＝，t3＝． ···················· 10分

3232附加题：解：（1）8； ···················································································· 5分

（2）2． ···················································································· 10分

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