- Cinh hoa & hai b6n : dd thi hdm sd 1, - ,1n TAt nhiOn ngudi lAp trinh phii chon h€ s6 a v}
khoing x6c dinh cira him sd cho thich h-o. p. 3) Binh hoa: Mdt cong Hypeb6l6it mOt tdng
trbn xoay ki hi0u le (Hr). Mat do m6t Hypebol
quay xung quanh truc vd tiOu c[ra n6.
Mat (Hr) md chring ta thubng gap 6 cdc lSng
hoa"cdn c6 thd tao nOn bbi cdc dudng thing
(trong mdt dip thich hqp, chfng tOi xin gi6i
thiOu chi tidt hon vd mit cong nly).
4) Ba chidc dAn bng 6 phia ffAn : Chrtnght
cdc mat gid cdu, PT cira c6,c mitt ndy trong hO
toa d6 D6-cric vuOng g6c Oxyz lit :
Mat gie cdu do dubng cong phing (trong mat
phing xOz) c6 phuong trinh
f x = asinu
I
) f ,(,,)l (6)
l, =rl cosa+lnl ts- ll
r L ("2/l
quay xung quanh trtc Oz.
So di goi li mat gii cdu v\ d6 cong Gauss tai moi didm tr€n mrt li m6t sd khong ddi 1gi6ng
mat cdu 6 ch5 d6) nhrmg lai th sd am (d0 cong Gauss tai moi didm cfra mdt cdu li sd duong
kh6ng Adil. '
Ilinh hoc tron mat gii cdu c6 nhidu didu li thri
nhmg chring t6i chua trinh bly trong pham vi
bli nhy. [x = [x = asinrr.cos r' (5) l):asma.stnl lr=r[.orr*,r( I/)l I L [,,;J]
Dd c6 hinh dang "chidc ddn ldng" ta chon
, q,PnP 6
Gidi ddp bdi :
AI DUNG AI SAI ?
H5a ra kh0ng phAi chi c6 hai ban A vh B tranh
luAn mh c6c b=an grli thu vd Tba soan cfrng c5 nfridu V kien kh6c nhau' Mot s6 it ban n6i ban A
ffig, irt sd kh6c cho rang hai ban A.vh B ddu
siAi"dfne nhmg thidu nghiOm, cbn da sd ci{c
Bii",,i,:i,i.uer dtirtp rang ci hai ban A vh B ddu
sai vi khong xet ?tr truong hgp n€n ddu thi€u nghiOm. Tu! nhi0n sai ldm cira cA hai ban A, B
dEu xuait pnat tU vi6c 6p dung tinh chdt cfra ddy
ti so bans. nhu, o:t='*'=1-', md kltotrg'-"---bdb+tlb-d '-"---bdb+tlb-d
cldt cti€u kiArt tudc ld b+d + 0 vh b-d + 0 (n€u tr6i lai ta d6n cldn bidu thrlc khOng c5 nghia)'
Khi giii trudi tien cdn dat didu ki€n ati uitiu
. .5x+3 3v-8 5x+9Y-21 ,,,rhricd€bdi -" -= " =--^ -(l,} rhricd€bdi -" -= " =--^ -(l,}
c5 nghia, d6 ld x * 0.
. Ldi giAi dring theo c6ch ctra ban B nhu sau :
Ap dung tinh chat ctra ddy ti sd bang nhau d6i
r,6i (1) duoc
5.r+3 3v-8 5x+3+9Y-24 5x+9Y-21 ,",
9 5 9+15 24
TiI (2) vd didu ki6n (1) ta c6
5x+9y-21 _5x+9Y-21
24 8,rX6r hai trudng hoP : X6r hai trudng hoP :
a) Ndu 8x + 24 thi tir (3) suy ra 5x+9y1-l = O'
Thay vho (2) cluoc 5,r + 3 - 3y - B = 0 dAn dOn
x=-315,y=813.
b) Ndu 8x = 24vd 5x + 9Y -21 + 0 thi x = 3 thay vdo (2) dugc 3Y - 8 = 10, suy ru Y = 6'
Nghi6m ndy th6a m6n 5;r + 9Y - 2l + 0'
V4y bli todn c6 hai nghiOm (x, Y) ln(-315,8/3) vd (3, 6). (-315,8/3) vd (3, 6).
o Ldi giAi dring theo cilch ctra ban A nhu sau :
X6t hai truhng hoP :
a) Ndu 8x = t hay x = 9/8 thay vho (1) duoc
t = 813 nhrmg (9/8, 8/3) khOng th6a mdn (1).
b) Ndu 8x * 9 thi 6p dung tinh chdt cira ddy ti
s6 bang nhau vito (1) duoc
(t 3 \ra(3v-8)l'- " l=0 ra(3v-8)l'- " l=0
\5 8x-9)
Tt d5 c6 y, = B/3 thaY vbo (1) tim duocxr = -315 vd x, = 3 thay vho (1) tim duoc !z'= 6' xr = -315 vd x, = 3 thay vho (1) tim duoc !z'= 6'
Cfrng c6 thd x6t hai trudng hop 8x = 5 vd
Bx + 5 vh giii tuong tu nhu tren'
C6c ban thm trong tdi gioi ld :
Th6i Nguy6n: Ngryen Hong Pltortg, Torln 10'
THPf chuydn Thrii Nguycn : Hi Tiry : Ngttyitt
Anh Tti,9B, THCS Xguye, Thuong Hidn, Ung
io", liai Hodng son,- 1k6, THCS Le Loi' Hd
DOns: Hunc Yen : Ngrr-vfrr TliThivTrattg'14'
THiS uintr"uAi, Van-Lam ; Nghe An: Ngtrvlrr Thanh Tudn, lOAl, K33, THIrf chuy0n Phan BOi Cfrar, Virn'l Vinh Long z Dtong Minh Tinn,
llTL, THPI NguY6n Binh KhiOm'
VANKHANH
ST UUNC CONG THUC VECTONHANH GON ! NHANH GON !
Trong gid luyOn tAp vd hinh hoc khOng gian tOi cho hoc sinh giii bni todn sau :
Trong kh\ng gian (Oryz) cho tam gidc -ABC
c6 toa"cta cdirtinh lii A (2; 3-; -l), B (0; -2; 5),