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        1. 過x軸上的動點(diǎn)A(a,0).引拋物線的兩條切線AP.AQ.P.Q為切點(diǎn)(1)若切線AP.AQ的斜率分別為k1.k2.求證k1?k2為定值;(2)求證:直線PQ過定點(diǎn); 查看更多

           

          題目列表(包括答案和解析)

          過x軸上的動點(diǎn)A(a,0)引拋物線y=x2+1的兩切線AP,AQ.P,Q為切點(diǎn).
          (I)求切線AP,AQ的方程;
          (Ⅱ)求證直線PQ過定點(diǎn);
          (III)若a≠0,試求
          S△APQ|OA|
          的最小值.

          查看答案和解析>>

          過x軸上的動點(diǎn)A(a,0)引拋物線y=x2+1的兩切線AP,AQ.P,Q為切點(diǎn).
          (I)求切線AP,AQ的方程;
          (Ⅱ)求證直線PQ過定點(diǎn);
          (III)若a≠0,試求
          S△APQ
          |OA|
          的最小值.

          查看答案和解析>>

          過x軸上的動點(diǎn)A(a,0)引拋物線y=x2+1的兩切線AP,AQ.P,Q為切點(diǎn).
          (I)求切線AP,AQ的方程;
          (Ⅱ)求證直線PQ過定點(diǎn);
          (III)若a≠0,試求的最小值.

          查看答案和解析>>

          過x軸上的動點(diǎn)A(a,0)的拋物線y=x2+1引兩切線AP、AQ,P、Q為切點(diǎn).
          (1)若切線AP,AQ的斜率分別為k1,k2,求證:k1•k2為定值;
          (2)求證:直線PQ過定點(diǎn);
          (3)若a≠0,試求S△APQ:|OA|的最小值.

          查看答案和解析>>

          過x軸上的動點(diǎn)A(a,0)的拋物線y=x2+1引兩切線AP、AQ,P、Q為切點(diǎn).
          (1)若切線AP,AQ的斜率分別為k1,k2,求證:k1k2為定值;
          (2)求證:直線PQ過定點(diǎn);
          (3)若a≠0,試求S△APQ:|OA|的最小值.

          查看答案和解析>>

          一.選擇題

          1―5  CBABA   6―10  CADDA

          二.填空題

          11.       12.()       13.2          14.         15.

          16.(1,4)

          三.解答題

          數(shù)學(xué)理數(shù)學(xué)理17,解:①         =2(1,0)                      (2分)             

                  ?,                                        (4分)

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          ?

                  cos              =

           

                  由,  ,    即B=              (6分)

                                                         (7分)

                                                                  (9分)

                                                                  (11分)

          的取值范圍是(,1                                                      (13分)

          18.解:①設(shè)雙曲線方程為:  ()                                 (1分)

          由橢圓,求得兩焦點(diǎn),                                           (3分)

          ,又為一條漸近線

          , 解得:                                                     (5分)

                                                              (6分)

          ②設(shè),則                                                      (7分)

                

          ?                             (9分)

          ,  ?              (10分)

                                                          (11分)

            ?

          ?                                        (13分)

            1.   單減區(qū)間為[]        (6分)

               

              ②(i)當(dāng)                                                      (8分)

              (ii)當(dāng)

              ,  (),

              則有                                                                     (10分)

              ,

                                                             (11分)

                在(0,1]上單調(diào)遞減                     (12分)

                                                               (13分)

              20.解:①       

                                                                      (2分)

              從而數(shù)列{}是首項(xiàng)為1,公差為C的等差數(shù)列

                即                                (4分)

               

                 即………………※              (6分)

              當(dāng)n=1時(shí),由※得:c<0                                                    (7分)

              當(dāng)n=2時(shí),由※得:                                                 (8分)

              當(dāng)n=3時(shí),由※得:                                                 (9分)

              當(dāng)

                  (

                                                        (11分)

                                       (12分)

              綜上分析可知,滿足條件的實(shí)數(shù)c不存在.                                    (13分)

              21.解:①設(shè)過A作拋物線的切線斜率為K,則切線方程:

                                                                              (2分)

                  即

                                                                                                                 (3分)

              ②設(shè)   又

                   

                                                                       (4分)

              同理可得 

                                                              (5分)

              又兩切點(diǎn)交于  ,

                                             (6分)

              ③由  可得:

               

                                                              (8分)

                                (9分)

               

              當(dāng) 

              當(dāng) 

                                                                   (11分)

              當(dāng)且僅當(dāng),取 “=”,此時(shí)

                                                     (12分)

              22.①證明:由   

                即證

                ()                                    (1分)

              當(dāng)  

                    即:                          (3分)

                ()    

              當(dāng)   

                 

                                                                       (6分)

              ②由      

              數(shù)列

                                                            (8分)

              由①可知, 

                                  (10分)

              由錯(cuò)位相減法得:                                       (11分)

                                                  (12分)