问题 解答题

已知△ABC的顶点A(0,1),AB边上的中线CD所在的直线方程为2x-2y-1=0,AC边上的高BH所在直线的方程为y=0。

(1)求△ABC的顶点B、C的坐标;

(2)若圆M经过不同的三点A、B、P(m,0),且斜率为1的直线与圆M相切于点P,求圆M的方程。

答案

解:(1)AC边上的高BH所在直线的方程为y=0,所以,AC:x=0,

又CD:2x-2y-1=0,所以

设B(b,0),则AB的中点,代入方程2x-2y-1=0,解得b=2,所以B(2,0);

(2)由A(0,1),B(2,0)可得,圆M的弦AB的中垂线方程为4x-2y-3=0,注意到BP也是圆M的弦,所以,圆心在直线x=上,设圆心M坐标为

因为圆心M在直线上4x-2y-3=0,

所以2m-2n+1=0…………①,

又因为斜率为1的直线与圆M相切于点P,所以,即

整理得…………②,

由①②解得

所以,,半径

所以所求圆方程为

单项选择题 A1/A2型题
完形填空

三、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(A、B、C和D)中选出最佳选项,并在答题卡上将该项涂黑。

Everyone knows that a favorite food of people in the USA is the hamburger.

The favorite place to buy 36 is a fast-food restaurant. In these 37  , people 38 their food, wait just a few minutes, then when the food is ready they carry it to their tables by  39 . They can either 40 it in the restaurant or take the food out 41 a plastic box and eat it 42 home, at work, or in a park. At some restaurants people can drive up 43 a window. They 44 the food, and a worker hands it to them 45 the window. Then they 46 off and eat in their cars or 47 they like.

Hamburgers are not the 48 kind of food that fast-food restaurants 49 . 50 serve fish, or sandwiches, and also 51 , coffee, and so on.

Fast-food 52 are very popular because the service is 53 and the food is not expensive. For many people, this is very important. In the United States, about 50% of all married women with children work outside. They are often too busy or too tired to 54 dinner for the family at night, and fast-food restaurants are a 55 help to help.

Now there are fast-food restaurants all over the world.

36. A. hot dogs           B. hamburgers      C. bread            D. cakes

37. A. cafes                B. shops              C. restaurants    D. stores

38. A. need              B. order                  C. require      D. want

39. A. yourself           B. yourselves        C. themselves    D. oneself

40. A. eat                 B. get                  C. take           D. bring

41. A. on                B. in                   C. at           D. of

42. A. in                B. of                  C. at              D. on

43. A. before               B. to                 C. beside          D. under

44. A. bring                B. order                C. eat             D. have

45. A. beside          B. through                C. near                D. throughout

46. A. go            B. take                 C. drive            D. walk

47. A. whatever          B. wherever         C. whichever      D. whoever

48. A. only              B. any                  C. one           D. some

49. A. take            B. work              C. serve          D. do

50. A. Another         B. Other              C. Some               D. Anyone

51. A. wine                B. orange juice          C. soft drinks    D. beer

52. A. meals             B. restaurants        C. markets        D. shops

53. A. kind              B. well                  C. fast           D. strange

54. A. have          B. take               C. cook          D. eat

55. A. large          B. best                  C. great          D. importan