cho ducrng-lidno^v?.dicm A ra- trdn duong trdn.. Chrmg minh ring CM Ia tiep tuydn cua 1O.. Goi F ld giao di6m thf hai cira ducyng tron 9i"g.. kinh oD.va dudng trdn ngoai ti6p tam gi6c oi
Trang 1UBNN riNs HA NAM or rru ruyEN sINH Lop 10 THpr NAnr Hec 20ts - z0t6
sO GrAo pUC vA DAo rAo M6n: To6n
op cuiNu rHrlc
c6u 1 (2,0 cti€m)
Thdi gian ldm bdi; t20 philt, kh6ng ke thdi gianphdt d€
2
2-rlx
a) Gi6i phuong trinh 5x
b) Giei hd phuong trinh
Cf,u 3 (1,5 di€m)
Trong mpt phing tga d6 Oxy cho parabol (p): ,- _ii
y = 3mx - 3 (v6i m ld tham s6) ., ,l
'-6x-8=0.
I( *3)(y* 2)=7 +xy [(**l)(v* t)=*y*2.
a) Rut gon bi6u thric A = rA - 7Ji + S",60 .
b)Chobi6uthricB=^-G* -1 (v6i x>0 vd x +4).
Riit ggn B
Ciu 2 (1,5 tti€m)
x-4
vdtimxdC B=1.
i,i '1, '
':'
vd dubng thdng (d):
a) Tirn m d6 ducrng thing (d) di qua di6m A(1; 3)
b) Xdc dinh c6c giStri cua m
9i (d) cet (P) tq\:nitdi6m ph6n bi6t sao cho t6ng2 tung dQ cua hai giao di6m d6 bing -10
cho ducrng-lidn(o)^v?.dicm A ra- trdn duong trdn 9qi o ld ti6p tuy5n cira (o) laiA, rr6n d l6ydi6m D (D kh6ngt*ns v6{ A), k6 ii6t66r r; u, r.D (e iJdia;,
B kh6ng trung v6i A) ;:'
a) Chfng -j* ring tf gidc AOBD n6i ti6p.
b) Tr6n tia doi cria tia BA l6y di6m C Ke bH vuong g6c v6i OC (H thu6c OC) Gqi I ld giao dicm cira ae ;5 oo "ch;G -i"r, *"g oH.oc = oI.oD.
c) Gqi M la.giao di6m cua DH v6icung nho AB cria (O) Chrmg minh ring CM
Ia tiep tuydn cua 1O).
+ \ d).Gqi E l+- gi.uo diem cria DH vd CI Goi F ld giao di6m thf hai cira ducyng tron
9i"g kinh oD.va dudng trdn ngoai ti6p tam gi6c oirra chrmg minh rdng o, E, F
thang hang
Ciu 5.(!1,0 Aiem1.
, ,.: rt-:tt, , @ho x, y ld c5c s6 thuc duong thoa m6n x + 3y _< l0.
: ' D6u
ding thr rayl;*I;J",
- HBT
-Girim thi tht nh6t: Gi6m thi thrl hai:
Trang 2HT.IONG OAX CAr Or-rWEN SINH LOP 10 THPT riNrr HA NAM
NAM HQC 20ts _2016 Mdn: Todn.
NQi dung
Ta co l': (-3)' - 5(-8) = 49 > O tr ,,
prc6hainghiemph6nbi6t x, -3+7=z; i
''*
4.
)55
I(^*3Xy +2)-z*
, ,:., 4:-i
lZx +3y = I lZ* +3v = I
al
€1 <f<
[x+y=1 l.:x+3y=3
' ; lt';'.
(u
-)
l/\-L
r-r \-,|J
lv=-1
w
Vay h.g phuong trinh c6 nghi6m duy nh6t (x; y) : (2; _1).
Dtrong thdng (d) di qua A(
Phuong trinh hodnh d0 Siu
-x' =3mx -3 <+ x2 +3mx-3 = 0 (*)
Ta c6 L =9m2 +12 > 0, v6i moi m n6n phucrng trinh (*) c6 hai nghidm ph6n bi6t Do d6 ducrng thing (d) vd parabol (p) c6t nhau tqihaidiCm (x,,y,) vd
(*r,yr) fneo dinh ly Vi-6t ta c6 xr + x2 = -3m i Xr.Xz - _3 .
Trang 3Theo bdi ra ta c6 yr * yz= -10 o _^i _i = -10 e (", + *rl'
- 2xrx, Dod6 9m2 +6=10<+m -*?
DA vd DB te c6c ti6p tuy-6n@lO;,ren 6BDE
Xdt tf gi5c AOB,
:U' d"t5 * OD = 1g00, md hai g6c ndy 6 vi tri aOi aien
n6n tir gi6c AOBpail,i tiep.
b)
Theo tinh clr6j.'hei figp
^
gi6c cria D Do d6 tam gi6c ABD cdn taiD c6 Do re ducrng phdn gi6c n€n ddng ,,, thcyi ld ducrng -ic) trung tryc usv.r .
"xdt AoIC vd AOI{D c6 5id = ofu = 900; chung f6D n6n
AOIC.,,AOFID(g.g)
OI OC
OH OD
Xdt tam giSc AOD vu6ng tai A c6 AI ld
(2)
Ma OM = OA (ld b6n kinh (O) (3)
Trang 4Tt (1), (2) vd(3) suy ra OM2 = OH.OC = OM OH = OM.OC
Xdt AOHM vd AOMC
AOHM.,,AOMC(c.g.c) .
+ OMa - 6id = 900 n6n CM ld tiiip tuy6n cta (O)
c6 chung Moa; gIuI = oc ,c,
OH OM
Do OMC = OIC = 900 n6n tri gi6c OIMC n6i ti6p ducrng trdn ducrng GF
,o.,nia-l.
Dudng trdn ngopi tiop tam gi6c cIM ld duong trdn ducrng kinh oc.
suy ra OFC = 900.
,]:1||| , :.|
Mpt kh6c ta c6 oFD = 900 Nhu v6y G-, m rc '' uisJv rabadiem C, F,
.'t "a
a :.
Xdt tam gi6c ocD c6.ba dudng cao cH, oq di,md c6 E ld giao di6m cH,
DI n6n ba di6m O, E,'F thing hdng.
C6ch 1.Ap dung bgjtoet,i.
2727^f2?n2.27
_++_L*3v > 3l_L.4.5
CQng cdc bdp d.tngthuc ( 1) vd (2) tadugc
/\
,[* -#)+(x +:v) >30 e r[#
#)>30-(x+3y) = 2e
x +3:!r,'<10)
127
<]-/-+-/->10.
D6u ding thtic xay ra khi vd chi *'
t;=;
C6ch 2 Ap dUng b6t tang thric Bunhiacopski , ta c6
I * 27 _ 1 _3:27 _- (t+e)' 1oo
(vi
(, E #$y) = (r' + r'X* + 3y) < 100
= J* *3$y< 10 (2)
Trang 5Tir (1) va (2) suy ra ** +> 10.