?????????

admin

???2015?????????��??????

2015?????????��??????

1??2015???22? ????x2?2y2?1?????????l1?l2???????A?

B?C?D???AOC????S.

?1??A(x1,y1)?C(x2,y2)??A?C??????C???l1???????

S?2|x1y2?x2y1|?

?2??l1:y?kx?C(

1,)?S???k???

333

?3??l1?l2??????m??m???????l1?l2???????S????. ???? ???????

??????1???????l1????y?

y1

x?

x1

?2????l1????k???l1?????y?kx?

?y?kx1

x????????2?????? y22

x?2y?1?2k?

???????x1?

1?2k

2

??y1?

k?2k

2

?

??S?

1131|x1y2?x2y1|??|x1?y1|?? 2233

??|x1?y1|?

2|k?1|

? ?

232k?1

??k??1?k??

1. 5

m? k

?3????????l1????k????l2????

?y?kx1

???l1?????y?kx???????2?????? x??y22

x?2y?1?2k?

???????x1?

1?2k

2

??y1?

k?2k

2

?

????x2?

kk?2m

2

2

?y2?

mk?2m

2

2

?

11|m?k2|

??S?|x1y2?x2y1|???

22(1?2k2)(k2?2m2)

?

|m?k2|(1?2k)(k?2m)

2

2

2

?c?????

??(m?k2)2?c2(k2?2k4?2m2?4k2m2)? ??k4?2mk2?m2?c2[2k4?(1?4m2)k2?2m2]? ??????????

2

??2c?1

??????2? 2

??c(1?4m)??2m

?c2?1

2?

S???????? 1

4?m??

2?

????m??

12

?S?. 24

???????l1?l2????????mx1x2??y1y2?

??mx1x2?y1y2?mx1x2y1y2?

222

2

2

y1yyy

?2??12?m? x2x1x1x2

??A(x1,y1)?C(x2,y2)???x?2y?1??

22

22222222

??(x1?2y12)(x2?2y2)?x12x2?4y12y2?2(x12y2?x2y1)?1?

?(

1222

?4m)x1x2y1y2?2(x12y2?x2y1)?1? m

2222

??x1y2?x2y1?2x1x2y1y2?(x1y2?x2y1)2

11

[1?(4m?)x1x2y1y2]?2x1x2y1y2 2m11

?2)x1x2y1y2? ??(2m?

22m

?

??S??????|x1y2?x2y1|???? ???2m?

1

?2?0??? 2m

??m??

12???S?.24

12

?S?.24

????m??

2

2??2015???21?????x?2y?1?????????l1?l2???????A?

2

B?C?D??????????ABCD????S.

?1??A(x1,y1)?C(x2,y2)??A?C??????C???l1???????

S?2|x1y2?x2y1|?

?2??l1?l2???????????

1

????S??. 2

?2????????l1????k????l2????????l1?????y?kx???????

1? 2k

?y?kx?x?2y?1

k?2k

2

22

???y??x??

1?2k

2

?

???????x1?

1?2k

2

??y1?

?

??4x1x2y1y2?2(x1y2?x2y1)?1? ??(x1y2?x2y1)?

2

2222

12??|x1y2?x2y1|?? 22

??S?2|x1y2?x2y1|?2.

3??2015????20?????C:x?3y?3???D?1,0???????2,1?????

2

2

??C???????????????x?3????? ??????C?????

?????????x???????????

?????????????D?????????????

?????1

????

?2?1??3???BM???DE??.

???????????????????????????????????????????????????????????????????????.???????????????????a?b?c??????e?

c

?????????????ABa

????????A?B????????AE????????AE?x=3???M??????M???????B??M???????BM???????????AB??????????????????????????????????????????????AB???AE????????????AB???????????x1?x2?x1x2????kBM?1?????????0????kBM?kDE???????.

x2

?y2?1.

??????????C??????3

??a?b?

1?c?

????C

????e?

c?. a?????AB??D(1,0)????x??????A(1,y1)?B(1,?y1). ??AE????y?1?(1?y1)(x?2). ?x?3??M(3,2?y1). ????BM???kBM?

2?y1?y1

?1.

3?1

?????BM???DE??.????? ???AB??????????????kBM?1. ?????DE???kDE?

1?0

?1???BM//DE. 2?1

???AB????????????y?k(x?1)(k?1). ?A(x1,y1)?B(x2,y2)????AE????y?1?

y1?1

(x?2). x1?2

?x?3???M(3,

y1?x1?3

).

x1?2

????????????

????

?9????3?1????x-1?2+y2=1???????????A?B????AB???? A

?A?2x+y-3=0?B?2x-y-3=0?C?4x-y-3=0?D?4x+y-3=0

2y2?10?????C:2?2?1(a?b?

0)x2?y2?1????ab??????????????????????????16????C???

??D ?

2222yyyy?A???1 ?B???1 ?C???1?D???1 82126164205

2

2

2

2

2axy

4??F1?F2???E:2+2=1 (a?b?0)?????? ?P???x??????

3ba

????30�????????E?????C ?F2PF1

?A?

22

1234

?B? ?C? ?D? 2345

x2y2

10a?b1(a>b>0)?????F(1,0)???F???????A?B????

AB??????(1??1)??E???? ( D) x2y2

A?45361

x2y2

B3627?1

x2y2

C?27181

x2y2

D18?9?1

x2y2

?4????-=1???????????A

412

?A

??B?2?C

?D?1

x2y22

9. ????2?2?1??????????y=x+1 ?????????????

ab

????(D ).A.

5 B. 5C. D.5 42

x2y222

?8??????2?2?1?a>0,b>0??????????C?x+y-6x+5=0???

ab

??????????C?????????????A

x2y2x2y2

?A? ??1 ?B???1

5445x2y2x2y2

?C??D???1 ??1

3663

?12??????E???????P(3,0)?E?????F???l?E???A?B????AB????N(?12,?15),?E?????B

x2y2x2y2x2y2x2y2

??1 (B) ??1 (C) ??1(D) ??1 (A)

36456354

?7????l????C????????C?????????l?C?? A,B???

AB?C?????2???C?????B

?A

?B

?C?2 ?D?3

x2y2

6.????2?2?

1B

ab

A.y=�2x B.y

= C.y??

1x

D.y?x 27.??l????C: x2=4y?????y?????l?C???????????C A.

48 B.2 C.

D. 333

x21

?y2?1?????????11????C1?y= x2(p?0)???????C2? 32p

C1???????M.?C1??M???????C2????????p=D

A.B

?C

?D

?

?13???????C????????????F(1?0)???l????C???A?B????AB?????2?2??????????_____ y=x ________. x2y25

4??????C:a?b?1(a?0?b?0)?????2??C??????? (C )

1

A?y=�

4

1

?B?y=

3

1

?C?y=�x

2

?D?y=�x

x2

3?????y2?1?????????????? c?

4

A?

24

B? C

D

55

3

,????C???? 2

7????????????C?????F?3,0?,?????( B )

x22x22x2y2x2y2

?1 B???1 A . D

??1 C???1 424525???C???1?0??????x?????????l:y?x?1??C?????

??22?????????l????????? x?y?3?0

x2y2

14????:2?2?1(a?b?0)?????????F1,F2????2c

????

ab

y?x?c)?????????M???MF1F2?2?MF2F1????????

???

?1____

?14?????????xOy????C?????????F1,F2? x?????

??

??l??? ??A,B?????ABF2????16???C????2

x2y2

??1 ? 168

2

13?????y?a????y?x?A,B????????????C????ABC

?????a??????_[1,??) __ _____?

?22???????14??

x2y2

???E: 2?2?1?a,b>0??M?2

?

???O??????

ab

?I????E????

?II???????????????????????????E??????A,B,?

OA?OB???????????????|AB |???????????????

x2y2

?22??:?1?????E: 2?2?1?a,b>0??M?2

?

,1)??,

ab2?4?11

??1?222???a2?8x2y2?ab?a8

??1 ?????????2??E????84?b?4?6?1?1?1?1

???a2b2?b24

?2???????????????????????????E??????

?y?kx?m

?

A,B,?OA?OB,?????????y?kx?m?????x2y2?

?1??4?8

x2?2(kx?m)2?8,?(1?2k2)x2?4kmx?2m2?8?0,

??=16k2m2?4(1?2k2)(2m2?8)?8(8k2?m2?4)?0,?8k?m?4?0

2

2

4km?

x?x??12??1?2k2?2

?xx?2m?8?121?2k2?

k2(2m2?8)4k2m22m2?8k2y1y2?(kx1?m)(kx2?m)?kx1x2?km(x1?x2)?m???m? 222

1?2k1?2k1?2k

2

2

,

???OA

O,B??x1x2?

2

2m2?8m2?8k2

??0,??y1?y20,?

1?2k21?2k2

?m2?23m2?822

3m?8k?8?0,??k??0?8k?m?4?0,???2,??

83m?8?

2

2

m2?

8,

?m?

?m?,????y?kx?m???????????3

m2m28????,

???????r?,r?,???r?223m?831?k1?

8

2

??x?y?

22

8,??????y?kx?

m???m?

?m?,???3x2y2??1?????

???????????

?x????84(

?

?(????OA?OB,??, ?????????3333

8

???????????????E??????A,B,?OA?OB. 3

x2?y2?

4km?

x?x??12??1?2k2

???, 2

?xx?2m?8?121?2k2?

4km22m2?88(8k2?m2?4)??(x1?x2)?(x1?x2)?4x1x2?(?,

)?4??

1?2k21?2k2(1?2k2)2

2

2

|AB|?

??

??

??k?

0?|AB|?

??4k?

2

1

?4?8??0?k2

11

?, 4k2?2?48

k

??

32321?[1?]?12,

332

4k?2?4

k

????????????

2007�2013?????

?????????????

1????x2?y????????

?A?4x?1?0 ?C?2x?1?0

?B?4y?1?0 ?D?2y?1?0

x2y2

2??????C?2?2?1(a?0,b?0),?C?????????C????????

ab

???????A?a

(B)b

(C)ab

22

(D)a?b

3

?y?m?0??x2?y2?2x?2?0??????m???? A

B

?

C

??

D

??

x2y2

4????2?2?1?a?0?b?0??????????F1?F2??F1?????

30

ab

??????????M???MF2???x????????????? A

B

C

D

2

2

5.????????60??????x?y?4y?0??????? ( )?A

?B?2 ?C

?D?

6.� m?n?0�?�??mx?ny?1?????y?????�?? ? ?A??????????B????????? ?C????? ?D) ??????????7.?????y?2px(p?0)?????(x?3)?y?16????p?????

2

2

2

2

2

?A?

1

2

2

?B?1 ?C?2 ?D?4

8?????????????????x??2?????????? ??A?y??8x ?B?y??4x ?C?y?8x ?D?y?4x 9. ???C:x?y?4x?0?l??P(3,0)?????? ?

?A?l?C???B? l?C???C?l?C???D???????????

22

10????M(a?b)??O?x?y?1?????ax?by?1??O??????()?

1

2

2

2

2

2

A???B??? C???D???? ?????

11. ??????????????l???????2?????4??????1?????? __________ ??

x2y2

??1?????__________? 12????

169

?????

13. (?????14?)

x2y26

????C:2?2=1(a?b?0)?????,??????????????3.

3ab

(?)???C???;

(?)???l???C??A?B???????O???l????????.

14???????12??

?????C?y?2x2???y?kx?2?C?A?B???M???AB?????M?x?????C??N?

?????????C??N?????AB???

?????????k?NANB?0??????k?????????????

15???????12??

???AOB??2

y2x2?????C????2?2?1(a?0,b?

0)????e??

ab2

??????????

? 5

?I? ????C????

(II)???P????C????A?B??????C?????????????????????AP??PB,??[,2]???AOB????????

2

13

16.??????13??

x2y2

?????C:2?2?1????A1,A2,B1,B2????F1,F2?

ab

A1B1?S

B1A1B2A2

?2S

B1F1B2F2

.

??????C????

????n ????????l??n?????P????????A, B??????

OP?1.????????l?OA?OB?0???????????l?????????

?????????.

17.??????12??

3x2y2

???C: 2?2?1?a?b?0????0?4???????

5ab

?1??C????

?2?????3?0?????

18. ??????13??

4

????C?????????? 5

x2

?y2?1???C2?C1?????????C1???????? ????C1:4

?1????C2????

?2??O???????A?B?????C1?C2??OB?2OA????AB????

19? (?????13?)????M(x?y)???l?x?4???????N(1,0)????2??

(1)???M???C????

(2)??P(0,3)???m???C??A?B????A?PB???????m????

3


??????????????????
?????http://www.850500.com/news/5468.html
?????,??!