THI TOÁN L6 2011(ĐDT HN)

TRIIGNG TF{PT'EAO DUY A pHAN Cffu DE T{' s'Egg g'EgEI&69 F{QC LAN TE{ti\rg { s4/2s9e} na0rq, ToAN KE{OI A Thoi gian: 180 phfi; kkhrcg kA thdi gian phtit di ctrtil{G DANr{ crro rAr cA qAc lni snm: I: Cho hdnr sd Y = xo -Znt'x'+1' thihdm sd khi.m = 1' gidc vudng cin 2) Tim m Ae aO tfrihdm sii c6 ba di€m cuc tri ld ba dinh ctian'rot tam 1) Kh&o s6t vd ve dO CSU trI: 2) Crai phuong trinh: 2(1+cosx)(cot'x+1)=*fi* CAU nffi: Tfnhtictrphanl : |r# ,/(;r + t)' (3x Ciu IV: +t) ' : CD: q Clro hinh ch6p S.ABCD c6 tlSy ABCD ld nua lpc gi6c ii€u v6i AD = 2a, AB = BC Hdy xAc dinh thiOt dudng cao SO ar[i vdi O ld trLrng diiim cria AD Tinh th6 tich hinh ch6p S.ABCD di0n m4t phing qua A vd vu6ng goc vdi SD cat hinh ch6p' : UAU V: 1 x' -2y>1 )(+x: y Thay vno (2) 1u "6' 2'[; -21s -1+ V"t - 14 = x -2 :> x2^-zx- I > o o lr' { ^-2r-l> =)x'-2x-1=0 1f ,'-14 so L(ABCD) u ) giA thirit (a) Vi SO I I sD =t (o) cat (seo) theo giao tuy6n ld cluong cao AH cfn NAD (ABCD) n6n (a) cit lenCO; theo giao tuy6n h ductng 0,50 thturg vuong g6c (SAD) tai A vay thi6t dien can opng x6c dlnh nhu sau: Trong m[t phang (ABCD) dlmg dubng thing vu6ng g6c vdi AD t4i A, ciit BC tpi F, cit CD t4i E, EH giao SC tpi J, FJ giao SB tpi N.:> AHJN le thi6t diQn cAn dpg CAU 1,00 v ll"-tl'-3x-ft 1(2) (}logrx+logr(x-1)(1 1:> y,= V,,q)= (:;t;-z):> phuong trinh (p) : lr,( o;1;-2) 3x + Y -'72 - l5:0 d( d' ; d' ) : d( Mr/e) ) (vi (P)// d2 vd 1P.,t \- / rr ri1.1 lt.z -t- Jl, 7.0 +12 - I sl +72 lo J59 t di€m bi6u di6n ld N(x; Y)' Do z' = 22+ - I :) lt ct +r (:a)' +(:a+ 1)' o' di€m bi6u di6n s0 phirc -t)tu= |(l*r)'(1)' TiI gin thi€t ltz + il' < zz +9' +bz +9.(2).Thay c6c gi6tri z' ld hinh trdn tdm b tu (1) va (2) ta c6: Tpp hqp c6c ,[',*), ban kinh R =+4 '\-' + )' ' (d):x-y+l:0 Vitit l4i (C) dudi dang ( x+i)2 + (y-2)' thiiSt goc MAB:600:> tAm I b5n kinh 6co g6c :5 :> (C) c6 tim I Gi;2) b6n kinh R=.F' Theo gi6 AMI = 300:> MI = 2iA:2R:216 VaV M phucrng trinh: (x+l)' * (y-2)' : QJt)z = 20' Do thuQc dudng trdn M e (d)n6n (x-v+l=0 lY=x+\ { nu't(" cta hQ: tem cua crlra M th6a mdn nghiQm L + -\2 l)' + (y -2)' =2a ''l(' + r)' + (x -t)' = zg :> *2 Viy :9 :) x: t c6 hai di6m VOi x:3:) y = V6i x: -3 M cAntim ld Mr( 3;4); Mz (3; -2)' :) y:'2 tga dQ viet tai (S): (x +z)' +(t-3)2 | (-2;3;0); R: ll3-* + z' =r3 -m = IN MN : n€n FrN = fn l -+ ,3_m_t;l IH @iAu kiQn m< 13.) M4t 29 ciu (S).An ti* c6 tim :, 1,00 @i6u kiQn m < -3) ld khoing c6ch tu I dtin d (d): 2x [2 Ixx+ 0' I v- -t D[t x: t:> ,(o ;1;-r) ed.d(t t 65 9=)m=-? IH= ( CAU 1,00 VIIb ,'y' a (x+1)3 (r+i)'' I,00 Md x +1 -, Ddu =L*Ll = riff ":t'xdv' € => (r + r)' ,-! fx=y-Z Maxnr: { lz=5 *' Tucrng to (v * [;)' 1)' ,!u,=>pcf3)' 4/ \27) ... z:-l.Timgi6tr!lcmnhAtcriabi6uthric: *tYt ' =- (x+yz)(t+rr)("*ry)' P Gi6m thicoi thi khdng giii thich gi th€m TR.EI{FNG TE{PT PAO PTTY BAp AN TtI - TI{ANG BIEM THI THU sAI x{QC tAN vY' Q'4184t281'1} rvlOrq : PiOm... dQ DAcdc vudng g6c Oxy cho dudng thing d: x - y + I : vd duong tron (C): x' + 1,' +2x-4y= Tim tga dQ diOm M thuQc ituong thing d mi qira d6 ta ke duoc hai duong thing tii5p xric vcyi ducrng trdn... ilTiong kh6ng gian v6i hQ iqadQ DAc6c vu6ng g6c Oxyz cho tludng thing: ()"-)rr-z+l-S*l=: vdrmdtcAu(S): x'+y'+?'*4x-6y*m=0 Timmdtiducrngthingdcftmgt a,1t*-^"-^" lx+2y-22-4 "au iS) t4i hai ctidrn M,