问题 填空题
已知两点M(1,
5
4
),N(-4,-
5
4
),给出下列曲线方程:
①4x+2y-1=0
②x2+y2=3
x2
2
+y2=1

x2
2
-y2=1

在曲线上存在P满足|MP|=|NP|的所有曲线方程是______.
答案

由M(1,

5
4
),N(-4,-
5
4
),

kMN=

5
4
-(-
5
4
)
1-(-4)
=
1
2
,M、N的中点坐标为(-
3
2
,0
),

∴MN的垂直平分线方程为y-0=-2(x+

3
2
),即y=-2x-3.

①∵直线y=-2x-3与直线4x+2y-1=0平行,∴直线4x+2y-1=0上不存在点P,使|MP|=|NP|;

②联立

y=-2x-3
x2+y2=3
,得5x2+12x+6=0,△=122-4×5×6=24>0.

∴直线y=-2x-3与x2+y2=3有交点,曲线x2+y2=3上存在点P满足|MP|=|NP|;

③联立

y=-2x-3
x2
2
+y2=1
,得9x2+24x+16=0,△=242-4×9×16=0.

∴直线y=-2x-3与

x2
2
+y2=1有交点,曲线
x2
2
+y2=1
上存在点P满足|MP|=|NP|;

④联立

y=-2x-3
x2
2
-y2=1
,得7x2+24x+20=0,△=242-4×7×20=16>0.

∴直线y=-2x-3与

x2
2
-y2=1有交点,曲线
x2
2
-y2=1
上存在点P满足|MP|=|NP|.

∴曲线上存在P满足|MP|=|NP|的所有曲线方程是②③④.

故答案为:②③④.

完形填空

第二节:完形填空(共20小题。每小题1.5分,满分30分)

阅读下面短文,掌握其大意,然后从36-55各题所给的四个选项中,选出最佳答案。

Once I thought love meant flowers, gifts and sweet kisses. So, I really   36   whether there is love between my parents. Every day they are very busy   37   to earn money to pay the high schooling for me. They don't act in the   38   ways that I read in books or I see on TV, and sending flowers to each other on Valentine's Day is even   39  .

One day, my mother was sewing a quilt. I asked her if there was   40   between them. She paused her work and raised her head with   41  . Then she bowed her head and  42  sewing the quilt. I was very   43   because I thought I had hurt her. But after a few minutes she said, “Look at this thread. Sometimes it   44  ,but most of the time it disappears in the quilt. If life is a quilt, then love should be a thread. It can   45   be seen anywhere or anytime, but it's really there, and makes the quilt   46  ”. I listened carefully but I couldn't understand her   47   the next spring..

My mother suddenly got sick seriously and had to stay in the hospital for a one-month treatment. Every morning and dusk after she   48   from the hospital, my father   49   my mother walking slowly on the country road. There were many beautiful flowers, green grass and trees, and the sun gently glistened them   50   the leaves. All of these   51   the most beautiful picture in the world.   52   their eyes, I know they love each other deeply. From this experience, I   53   that love was just a   54   in the quilt of our life. Love is   55  , making life strong and warm.

36. A. believe               B. hesitate             C. doubt                         D. ignore

37. A. keeping                 B. trying               C. willing                 D. learning

38. A. romantic             B. magic               C. formal                        D. special

39. A. unsuitable           B. impolite            C. uneasy                        D. impossible

40. A. difference           B. love                  C. similarity            D. fight

41. A. surprise                 B. anger                C. smile                   D. calm

42. A. finished                 B. forgot               C. continued             D. considered

43. A. excited               B. worried             C. shocked                D. disappointed

44. A. exists                  B. works               C. breaks                  D. appears

45. A. easily                 B. hardly           C. simply                        D. usually

46. A. long-lasting         B. long-dated         C. long-suffering       D. long-winded

47. A. after                   B. before               C. until                    D. since

48. A. returned                 B. escaped             C. remained              D. heard

49. A. led                            B. let                   C. supported             D. helped

50. A. from                  B. through             C. across                  D. throughout

51. A. made up             B. made with         C. made into             D. made of

52. A. Seeing                B. Watching           C. Reading               D. Checking

53. A. expected             B. admitted            C. noticed                 D. realized

54. A. material                B. design                 C. color                       D. thread

55. A. everywhere         B. inside                C. anywhere             D. outside

单项选择题 A1/A2型题