HÌNH HỌC LỚP 10 NÂNG CAO

CHUONG QnytoaoHiiVirang \Vi tri ciia dioi/ QivilioaoDHiiViniig PHUONG PHAP TOA D6 TRONG MAT PHANG Bing cdch dua vdo mat pharig m^t h§ true toa dd, mdi vecto, m6i diem tren mat phlng dd diu dugc xdc /2jc-3y + = vd A2 : JC + 3y - >j^ = ; 6) Al : X - 3y + = vd A2 : -2x + 6y + = ; c)Ai : , ; c + y - = vd A2: l,4jc + y - = Cau hoi vd bai tap Trong cdc mdnh di sau, menh dl nao diing ? a) Dudng thing song song vdi true Ox ed phuong trinh y = mim^O); v b) Dudng thing cd phuong trinh x = m + song song vdi true Oy ; c) Phuong trinh y = kx + b la phuong trinh cua dudfng thing ; d) Mgi dudng thing diu cd phuong tnnh dang y = kx + b; e) Dudng thing di qua hai dilm Aia ; 0) vk BiO ; b) ed phuong tnnh ^ + ^ = a b Vilt phuong trinh tdng quat cua , a) Dudfng thing Ox ; b) Dudng thing Oy ; c) Dudng thing di qua M(JCO ; yo) vd song song vcAOx; d) Dudng thing di qua M(JCO ; yo) vd vudng gdc vdi Ox ; e) Dudng thing OM, vdi M(jco ; yo) khdc dilm O 79 Cho tam gidc ABC cd phuong tnnh cdc ducfng thing AB, BC, CA la AF;2jc-3y-l=0; FC • JC + 3y + = ; CA ; 5x - 2y + = Vilt phuong trinh tdng qudt ciia dudng cao ke tit dinh B Cho hai dilm F(4 ; 0), 2(0 ; -2) a) Viet phuong trinh tdng qudt cua dudfng thing di qua dilm A(3 ; 2) vd song song vdi dudng thing PQ ; b) Vilt phuong trinh tdng qudt cua dudng trung true cua doan thing PQ Cho dudng thing d cd phuong trinh jc - y = va dilm M(2 ; 1) a) Vilt phuong trinh tdng qudt cua dudng thing dd'i xiing v6i dudng thing d qua dilm M b) Tim hinh chiiu ciia dilm M tren dudng thing d Xet vi tri tuong ddi cua mdi cap dudfng thing sau vd tim giao dilm (nlu cd) cua chung a) 2JC - 5y + = vd 5JC + 2y - = ; b) X - 3y + = va 0,5JC - l,5y + = ; c) IOJC + 2y - = va 5JC + y - 1,5 = PHl/ONG TRINH THAM s6 CUA Dl/dNG T H A N G y —• "1 Vecto chi phirong cua dirdng thing Tren hinh 70, vecto MI khdc 0, cd gid la A/ dudng thing A ; vecto 1*2 l^dc 0, cd gid song song vdi A Khi dd ta ggi uy, 02 Ik eac vecto chi phuong cua dudng thing A 80 ^ '"2 X Hinh 70 DjNH NGHiA I Vecta u khdc 0, cd gid song song hodc trung v&i du&ng thdng A dugc ggi Id vecta chi phuang cua A ?l1 Vecta chi phuang vd vecta phdp tuyi'n cua mdt dudng thdng quan he v&i nhu the ndo ? ?2l Vi vecta u = ib ; - a) la mdt vecta chi phuang cua du&ng thdng cd phuang trinh ax + by + c = 01 Phirong trinh tham so cua dirdng thang Bai toan Trong mat phdng toq Oxy, cho du&ng thdng A di qua diem lixQ ; yo) vd cd vecta chi phuang U =ia ; b) Hdy tim diiu kiin ciia xvdy dediim Mix ; y) ndm tren A 3" ii^^ (Di giiti bai toan) *Oilm M nam trdn A vd chi vectd !M ciing phUdng vdi vectd U (h 71), tiic Id cd sd t cho 1M jnAix-,y) y^Kxo -, yo) = tii / X Hdy vilt toa dp ciia IM vd cQa tu rdi so sdnh Hinh 71 cdc toa dp cCia hai vectd Tix hoat ddng trdn suy : Dilu kien cdn va du dl Mix ; y) thudc A la cd sd t cho \x = XQ + at [y = yo + bt iP +P * 0) (1) He (1) dugc ggi Ik phuang trinh tham sd cua dudng thing A, vdi tham sd t CHUY Vdi mdi gid tri eua tham sd t, ta tfnh dugc jc va y tuf he (1), tiic la cd dugc dilm M(;c; y) nim trdn A Nguge lai, nlu dilm Mix ; y) nim tren A thi cd mdt sd t cho x, y thoa man he (1) 81 l-HHIONCA ?3| Cho du&ng''thdng A cd phuang trinh tham sd' (x = + t [y = l-2t a) Hdy chi mdt vecta chi phuang ciia A b) Tim cdc diem cua A dng v&i cdc gid tri t = 0,t = -4,t= — c) Diem ndo cdc diem sau thudc A ? M ( l ; 3), A^(l; -5), F(0; 1), Q(0; 5) ^Cho dudng thing d cd phUdng trinh tong qudt 2jc - 3y - = a) Hay tim toa dp cCia mdt dilm thudc d va viet phUdng trinh tham sd cfla d 'x = + l,5t b)H§ cd phai Id phUdng trinh tham sd cOa d khdng ? c) Tim toa dp ciia dilm M thudc d cho OM = CHOY ( a^O,b^O ta di din X = Xn + at y = yo + bt ciia dudfng thing, nlu thi bing cdch khtr tham s61 tix hai phuong trinh trdn, ^^^U^^y-M a b ^a^O,b^O) (2) Hiuong trinh (2) dugc ggi Ik phuang trinh chinh tdc cua dudng thing Trong trudng hgp a = hoac = thi dudng thing khdng cd phuong trinh chfnh tic Vi du Viet phuang trinh tham sd, phuang trinh chinh tdc (ni'u cd) vd phuang trinh tong qudt cua du&ng thdng mdi tru&ng hgp sau a) Di qua diem A(l ; 1) vd song song v&i true hodnh ; b) Di qua diem F(2 ; -1) vd song song v&i true tung ; c) Di qua diem C(2 ; j vd vudng gdc v&i dudng thdng d : 5x-Iy+ = 82 a - HHIONCB Gidi a) Ehrdng thing cdn tim ed vecto chi phuong / = (1 ; 0) vd di qua A ndn nd ed x =I+t vk phuong tiinh tdng quat la y - = f Dudng thing khdng cd phuong trinh chfnh tie b) Dudng thing cdn tim ed vecto chi phuong j = (0 ; 1) nen khdng ed phuong trinh chfnh tie Do dudng thing dd di qua F ndn nd ed phuong rjc = trinh tham sd la I vk phuong trinh tdng quat lkx-2 [y = -l + t = e) Vecto phdp tuyin n = (5 ; -7) cua d cung la mdt vecto chi phuong cua dudng thing A cdn tim (do A d) Do dd phuong trinh tham sd eua A , fjc = + 5f ^ ^ u -^ u ^ ' A ,^ •« - la < va phuong trmh chinh tac eua A la [y = - 7f ' = y -1 -7 Tii phuong trinh chfnh tic (hoac tham sd) cua A, ta suy dugc phuong trinh tdng qudt cua A la 7JC + 5y - 19 = Vilt phuong trinh tham sd, phuong trinh chfnh tac (nlu cd) vd phUdng trinh tdng qudt cCia dudng thing di qua hai dilm Mi-4 ; 3) vd Nil ; -2) Cau hoi va bai tap Cho dudng thing A : | Hdi cae mdnh dl sau, menh dl [y = -2t • ndo sai ? a) Dilm A(-l ; -4) thudc A b) E)ilm F(8 ; 14) khdng thudc A, dilm C(8 ; -14) thudc A c) A cd vecto phdp tuyin n = (1 ; 2) d) A cd vecto chi phuong M = (1 ; -2) e) Phuong trinh "^ ~ = la phuong trinh chinh tic cua A -6 f) Phuong trinh ^ ^ - = — la phuong trinh chfnh tic eua A ^ 83 X V 18 Cap dilm ndo Id cdc tieu dilm ciia hypebol — = "> (B) (± Vi4 ; ) ; (D)(0; + Vl4) (A) (+ ; ) ; (C)(±2;0); 2 19 Cap dudng thing ndo la cdc dudng tiem can cua hypebol — =1? 25 16 (B)y = + | x ; (A)y = ± - x ; (C) = A ; ^^)^-^i2 , , V X 20 Cap dudng thang nao la cdc dudng chudn eua hypebol — - ^ (IP (A)x = ± ^ ; (B)x = ± - ^ ; q P iO x = ±-j=J= yjp+p = 1? r; (D)x = ± ^ ,2 , „2 {q^ +P^ 21 Dudng trdn nao ngoai tilp hinh chii nhat co sd eua hypebol (A)x^ + y^ = ; (C)x2 + y = ; X y -^^ = ? (B)x^ + y^ = ; (D)x^ + y^ = 22 Dilm nao la tidu dilm cua parabol y = 5x ? (A)F(5;0); (B) F (5 23 Dudng thing nao la dudng chudn eua parabol y = 4x ? (A)x = ; (B)x = - ; (C)x = ± l ; (D)x = - 24 Cdnic cd tam sai e = -7= la dudng nao ? V2 (A) Hypebol; (C)Elip; (B) Parabol; (D) Dudng trdn 123 Sai doc them BA DUONG CONIC TCr xa xUa, ngudi Hi Lap chufng minh dugc rang giao tuyen cCia mat ndn trdn xoay va mdt mdt phlng khdng di qua dinh ciia mdt ndn la dudng trdn hodc dudng cdnic (elip, hypebol, parabol) (h 98) Tieng Anh, tCr cone cd nghTa 1^ mdt ndn, do cd tu "dudng conic" Ducmg tron Parabol Hypebol Hinh 98 Ngay tCr d i u thdi ki A-llch-xdng-dd-ri (thdi cd Hi Lap), ngudi ta da bilt khd ddy dii ve cac dudng cdnic qua bd sach gdm quyin ciia A-pd-ld-ni-ut (262- 190 trUdc Cdng nguyen) Cudi thdi ki do, nha toan hoc Hi-pa-chi-a ( - sau Cdng nguyen) da cdng bd tdc phim "Ve cac dudng conic ciia A-pd-ld-ni-ut" Phai rat lau sau dd, den the ki XVII, ngudi ta mdi tim thdy nhOmg ting dung quan trgng ci!ia cac dudng dd sU phat trien ci!ia khoa hgc va kTthuat Ba dudng cdnic cdn cd nhieu tinh chat chung Tinh chat quang hgc la mot vi du : Mdt tia sang phat tix hidt tidu diem cCia elip (hay hypebol) sau dap vdo elip (hay hypebol) se bj hat lai theo mdt tia (tia phan xa) nam tren dudnig thing di qua tieu diem thii hai ciia elip (hay hypebol) (h 99) /" / I? \'' \ a) Hinh 99 124 Hinh 100 Vdi parabol, tia sdng phat tii tieu diem (tia tdi) chieu den mot diem cOa parabol se bj hat lai (tia phan xa) theo mdt tia song song (hodc triing) vdi true ciia parabol (h 100) Tinh chdt ndy cd nhieu ling dung, ching han : • D6n pha : Be mdt cda den pha la mdt mdt trdn xoay sinh bdi nidt cung parabol quay quanh true cCia nd, bdng den dugc ddt vi tri tieu dilm cua parabol dd (h 101) Hinh 101 • May viin vong v6 tuydn cung cd dang nhu den pha (h 102) Diem thu va phat tin hi§u ciia mdy dugc ddt vj tri tieu diem ciia parabol Hinh 102 Hinh 103 • Hinh 103 la md hinh mdt Id phan ling hat nhan dugc xay dung d MT Mdt ngodi ciia Id Id mdt trdn xoay tao bdi mdt cung cCia hypebol quay quanh true ao cCia nd Chiing ta da biet qu? dao cGa cac hanh tinh he Mdt Trdi la dudng elip Ddi Vdi cac ve tinh nhdn tao va cdc tdu vu tru, phdng len, ngUdi ta phai tao cho Chung cdVan tdc thich hop d l dugc quy dao Id elip, hypebol hodc parabol 125 Ngoai ra, ngudi ta cdn dng dung cdc tinh chdt cda ba dUdng conic cac nganh xdy dung, hang khdng, hang hai, (h 104) b) a) Hinh 104 BAI TAP N c u d i NAM Trdn hinh 105, ta ed tam gidc ABC vk cdc hinh vudng AA'FiF, FF'CiC CCAiA Chiing minh cdc ding thdc sau a) iAA + 'm')AC = 0; b) (AA' + BB' + CC').AC = ; c) AA + BB' + CC' = ; d) AFi +FCi +CAi = Cho tam giac ABC vudng tai A,AB = c, AC = ft Ggi M la dilm trdn canh BC cho CM = 2BM, N la dilm trdn canh AB cho BN = 2AN (h 106) a) Bilu thi cae vecto AM vk CN theo hai vecto AB vkAC h) Tim he thdc lien he giiia ft vd c cho AM CN 126 Hinh 106 Cho tam gidc AFC vdi AF = 4, AC = 5, FC = a) Tfnh cdc gdc A;B,C b) Tfnh dd ddi cdc dudng trung tuyin va dien tfch tam gidc c) Tfnh cac bdn kfnh dudng trdn ndi tilp va ngoai tilp tam gidc ABC Cho tam giac AFC a a) Tam gidc ABC cd tfnh chdt gi nlu a^ = ^ ^'^ b+c a 1 b) Bilt — = — + —, chiing minh rang 2sinA = sinF + sinC K h K Trong mat phing toa dd Oxy cho hai hinh chii nhat OACB vk OA'C'B' nhu hinh 107 Bilt A(a ; 0), A'ia'; 0), BiO ;ft),F'(0 ;ftO(a, a', ft, ft' la nhiing sd duong, a^a',b^ ft') a) Vilt phuong trinh cae dudng thing AF'vaA'F y b) Tim lien he giiia a, ft, a', ft' dl hai dudng thing AB' vk A'B cit Khi dd hay tim toa dd giao dilm / cua hai dudng thing dd B' B c) Chiing minh ring ba dilm /, C, C thing hdng d) Vdi dilu kidn ndo cua a, ft, a', ft' thi C Id trung dilm c i i a / C ? • , r' c A' A X Hinh 107 Trong mat phing toa dd Oxy cho hai dilm A(3 ; 4) va F(6 ; 0) a) Nhan xet gi vl tam gidc OAB ? Tfnh didn tfch cua tam giac dd b) Vilt phuofng trinh dudng trdn ngoai tilp tam giac OAB c) Vilt phuong trinh dudng phan giac tai dinh O eua tam giac OAB d) Vilt phuong trinh dudng trdn ndi tilp tam giac OAB Trong mat phing toa dd, vdi mdi sd m ^ 0, xet hai dilm Mi(- ; m) vk a) Vilt phuong trinh dudng thing M1M2 b) Tfnh khoang each tie gdc toa dd O tdi dudng thing M1M2 127 e) Chiing td rang dudng thing M1M2 ludn tilp xuc vdi mdt dudng trdn cd' dinh d) Ldy cae dilm Ai(-4 ; 0), A2(4 ; 0) Tim toa dd giao dilm / cua hai dudng thing A1M2 vd A2M1 e) Chiing minh ring m thay ddi, / ludn ludn nim trdn mdt elip (F) cd dinh Xac dinh toa dd tidu dilm cua elip y2 X Cho hypebol (//) cd phuong trinh — - ^^^ = 16 a) Viet phuofng trinh cdc dudng tidm cdn cua hypebol (//) b) Tfnh dien tfch hinh chii nhat co sd cua hypebol iH) e) Chiing minh rang cac dilm M ; - vd NiS ; 2yf3) diu thudc iH) d) Viet phuong trinh dudng thing A di qua M, N vk tim cdc giao dilm F, Q ciia A vdi hai dudng tidm cdn cua hypebol iH) e) Chiing minh ring cac trung dilm cua hai doan thing PQ vk MN triing Cho parabol (F) ed phuong trinh y = 4x a) Xac dinh toa dd tiiu dilm F va phuong trinh dudng chudn d ciia (F) b) Dudng thing A cd phuong trinh y = m (m ^ 0) ldn lugt cit d, Oy vk (F) tai cac dilm K, H, M Tim toa dd ciia ede dilm dd c) Ggi / la trung dilrn eua OH Vilt phuofng trinh dudng thing IM va chiing td rang dudng thing IM eat (F) tai mdt dilm nhdt d) Chiing minh ring M/ ± KF Tit dd suy MI la phdn gidc cua gdc KMF 128 HirdNGDAN-OAPSO ChUdng I M-^i-x ; — y) 36 a)Trong t4m cua tam giac la a) Sai; b) Dung ; c) Sai; d) Dung ; e) Diing ; G(0;l);b)£) = ( ; - l l ) ; c ) £ = ( - ; - ) d n tap chuong I • f) Sai Cac vecto a, d, v, y ciing phuong, d c vecto b, u cung phuong Cac cap vecto ciing hu6ng : a \z.v AB + CA = CB ; BA + CA = WiD la dilm d6i xdng cua -, d vay , b wku Cac cap vec to bang : a va v ; fc va « a) Sai; b) Ddng ; c) D u n g ; d) Sai; e) Dung ; f) Dung Hinh thoi a) Sai ; b) Dting 11 a) Sai ; b) Ddng ; c) Sai ; d) Ddng 12 M, N, P nkm trfin ducmg tron (O) cho CM, AN, BP la c i c dudng kfnh cua (O) 13 a) ICON ; b) 50N 16 a) Sai ; b) Dung ; c) Sai ; :d) Sai ; e) Dung 17 a) Tap rdng ; b) Tap g6m chi m6t trung dilm O ciia AB 21 loA + Ofil IOA-OBI IIOA^'-OB ; MN = OA BC = -a-2b ; ; BA + CB = CA ; CB-CA ; = AB ; = BE Bai t$p trdc nghidm chuong I + -OB ; ; CA = 2a + b 26 AA' + BB' + CC'' = 27 Chdng PQ + RS + fu ; GC =-a - b A) ; ^OA + OB + OC + dD = a) Af la dinh cua hinh binh hanh ABCM ; A' la trang dilm 3 ciia AD b) p = — ; a =— a) Ic = — ' ^ A a) Chdng minh AB v£l BC khSng cdng phuong ; b) D = (2 ; - ) ; c) £ = (-3 ;-5) MB = - -OA + OB AN = -OA + -OB AB = -a + b a^f2 dilm CB + BA = CA AB -CB = AB + BC =-AC -,BC-AB 28 22 OM = -OA+0OB 25 = qua ; (E ia dilm cho ABCE la hinh binh hanh) OA = OB Sur dung dang thdc —OA + 2,50B V6073 5a \30A + 40B\ yJSAl = C AB + BC = AC minh = 29 b), c), e) Dung ; ( C ) ; ( B ) ; ( D ) ; ( Q ; ( A ) ; (C): (A); (B); (B); 10 (A); 11 ( Q ; 12 (D): 13 (D); 14 (A) ; (D) ; 16 (B) ; 17 (D): 18 (B); 19 (D); 20 (A); 21 (B); 22 (B); 23 (B), Chuong 11 a) •^-V^-1 < • a) 2sin80° ; b) cosar a.b duong hai a), d) Sai 30 a = (-1 ; 0), fc = ( ; 5), vecto a , b khac va goc {a ,b)ht c=i3-,-4),d am hai vecto a , b khac va goc (a , b) = ( ; - , e = (0,15 ; 1,3), hon 90° ; ldn hon 90° ; bang hai vecto a va fe f = in ; - cos24°) a) M = (2 ; - ) ; b) J = ( - ; l ) ; c ) j t = , ; / = - , , ^ = - vudng goc 360° a) ^ ^ ^ ; b) ^ - y ^ - 10 a) Chu y ring hinh chie'u ciia vecto 33 Cdc menh di dung la a), c), e) ; Cac mfenh dd sai m b), d) 34, b) D = ( - ; 7) ; AB tren dudng thang Al la vecto AM ; b) JM Jl+ c) £ = U ; o J 35 Miix, - y), MjC ^; y) ^ BI =4R^ 12 Tap hop cac dilm M la dudng thing vudng goc vdi OB tai H, 129 O la trung dilm cua AB, H nam tren tia OB ChUdng III cho OH^— 13 a) A: = - ; b) ;fc = ±^^^^ 4a 14 a) Chu vi tam gidc la + 6v5 , dien tich Cac menh dl ddng la a), b), c ) ; Cdc menh.dl sai la d), e) a) >-= ; b) X = ; c) y - yo = (j-o *0) -, d) X - xo = 0; e) y^x- xoy = Ik 18 ; b) G = (0 ; 1), / / = Q ; i j , / =f ^; i j 2A: + b) 2A: 15 cos A = — , A « 50° 16 BC = 7.17 Ban 39 Cudng (BC = >/37 « 6,1 km) 19 a « 4,9 ; c « 5,5.20 i? * 3,5.22 AC * 857 m, BC » 969 m 24 m^ « 6,1 25 AD « 8,5 26 AC « 5,8 29 S « 16,3 33 a) C = 80°, b « 9,1, a « 12,3 ; b) B = 75°, a « 2,3, c =fc= 4,5 ; c) B = 20°, a « 26,0, fo « 13,8 ; d) A = 40°, » 212,3,'' c « 179,4 34 a) A = B = 63°, c « 5,7 ; b) a « 53,8, B « 36°, C « 57° ; c) c « 28,0, A » 11°, B « 39° 35 a) A « 43°, B « 61°, C « 76° ; b) A « 55°, B « 85°, C « 40° ; c) A « 34° ; B « 44° ; C « 102° 36 6,6 N 37.17,4 m 38.18,9 m n t^p chuong II Tap hop cac dilm M co thi Ik dudng trdn, dilm G hoac tap rdng theo cac gia tri cua Ic Bilu thi cdc vecto qua JB, JB', JC, AC 53; + — = a) X - 2y + = ; + y - = a) X - y - = ; J 3^ b) M'l —; - a) Hai dudng flidng cat 21 ddilim — ; — ; b) Hai dudng thang gong >^ 29 29 J song ; c) Hai dudng thing triing Cdc menh dl ddng 1^ b), d), e), f); Cdc menh dl sai la a), c) Cdc menh dl ddng 111 a), b), d), e) fx = - + 3r Menh de sai Ik c) a) -^ ; [y = 5t ^^^ = ^ -,5x-3y+l5 = 0-,h)r^'^ ; ' [y = l + t Khdng CO phuong trinh chfnh tac ; x - = ; c) 'x = -4 + 5t _ A : + _ J ' - _ ; x - y + = >' = l+3r 10.a) ^ ^ = ^ — ? b)A:-2y + = 0.11 a)Hai ^ -2 dudng thing song song ; b) Hai dudng thing cat tai (0 ; -13) ; c) Hai dudng thing '_ J ayflO a-JS a-i\Q a) BM = , BN = , MN = ; 4 5a^ b) ABMAf vudng cdn tai M, S = 16 av2 aVlO ^ /^ 7^ c) IC = -— , d) R = —— a) ie,f) « trung 12 a) (3 ; 1) ; b) ' ^^ V25 262 250 133 13 M = c) 169-' 169 18 61°56' ; b) /w = ^ ; c) n = - i ldn nh^t va chi C = 90° S = 96 , h^ = 16 ; /?= 10 ; 7-= 4.12 a) AB^ + CD^ = 8/?^ - 40P^ ; h) PA^ + PB^ + PC^ + PD'^ = 41^ Bai tap trac nghiem chuong II (B); (C); (A); (D); (A); (B); (B); (D); (C); 10 (B); 11 (A); 12 (C); 13 (B); 14 (A); 15 (C); 16 (C) C = 130 14 B 11'11, ( - { Y ; - —] 11 ^^ 25 97 18 20' 11 • 15 Cdc menh dl b), c), e) dung Hai menh dl a) va d) sai 16 43°36' 17 ax + by + c + hlc^+b^ =0 , ax + by+ c- hyja^ + b^ = IS x + 2y - 14 = ; >- - = 19 Khdng t6n tai 20 (1 + •J2)ix - 3) + (3- - 1) = ; i\-yl2)ix-3) + {y-\) = Q 21 a) b) \k d) Ddng ; c) Sai 22 a) (A: - )^ + (y - 3)^ = ; b) (X + 2f + / = 23 a) /(I ; 1), /? = ; cdc dudng tiem cdn )» = ± - A : ; b) Tieu dilm b) /(2 ; 3), /? = v n c) / f - ; l ] , Fii-5 ; 0), ^2(5 ; 0) Dd ddi true thuc 2a = Dd ddi true ao 2b = Phuong tnnh cdc dudng tiem I— « = iV33 - %Tr? vdi dilu kien |OT| < j — cdn y = ±-x ; c) Hai tieu dilm Id (-V10 ; 0) V8 vd (VlO ; 0) Dd dai true thuc bdng 6, dd dai true 24 (x - 3)^ + / = 8.25 a) (A: - 1)2 + (y - 1)2 = 1; bang Phuong trinh cdc dudng tiem can (;t - 5)2 + (y - 5)2 = 25 b) (jc-3)2 x2 y2 y = ±-x 38 - ^ ^ r = t B2 i^R ihpl - Y"lj "f ''^('' + 0^^('-fj =f I 26.(1 ;-2)vk f — ; - - j 27 a)3A:-3'+2Vro = v d x - ' - 2V1O =0;b)2A:-3'+ 2^5 = 39 a) — - ^ = 16 vjl2x-)'- 2>/5 = ; c ) > ' + = 0vdA: = •28 Im ^ 5| > 2VI0 : A vk («) khdng cat ; c) X Im + 5| = 2>/i0 : tilp xdc ; Iw + 5| < 2V1O : -2+-K\ cat 29 -2' '2' ) 2+vrii 30 a), b) va d) dung ; c) vd e) sai 31 a) Toa dd cdc tieu dilm la (+>/2T ; 0) ; Toa dd cac dinh Id (±5 ; 0) vd (0 ; ±2) Dd dai true ldn 2a = 10 dd ddi true be la 2fe = ; b) (±>/5 ; 0) (±3; 0) vd (0; 12); 2a = 6,2fc = ; c) (±V3 ; 0) (±2 ; 0) va (0 ; ±1), 2a = 4, 2fe = 2 32 a) — + ^ = 16 ;r2 20 16 3>/2 ylu\ va M2 (3^ sfu] 34 e « 0,07647 35 Tap hop dilm M la elip c6 phuong trinh wii ^ 27 13 ) 12 = 13 ^^— = 42 a), b) va d) sai; c) ddng 43 a)>'2=12A:;b)>'2 = x ; c ) / =±;c 44 2p 45 d(/ ; A) = - AB Dudng trdn dudng kinh AB tilp xuc vdi dudng chudn A 46 y= X +—X 47 a) Tieu dilm 4 F(3,5 ; 0), dudng chudn A: + 3,5 = ; b)TOudilm Fi(->/3 ; 0), dudng chudn Ai : A; + -=r = V3 x ^ c) j + Y = 1- 33 a) MN = \y^ -yt,\ = - ; b) M, y Tieu dilm F2 (Vs ; 0), dudng chu&i A2 : •+y-=\ b) 2 36 Cdc fJ [f, menh dl a), b), d) dung ; c) sai 37 a) TOu dilm fl(-Vl3 ; 0), F2(Vi3 ; 0) Dd ddi true thuc 2a = Dd ddi true ao 2b = Phuong trinh V3 = ; c) Tieu di6m Fii'-yflS ; 0), dudng chuin A, : A: + - = = TOu dilm F.iy/iS ; 0), Vis 14 dudng chudn AT : A: — i = = Vl5 On tap chuong III a) AJ, A2cat ; b) Aj // A2 ; c) Aj = A2 a) ^ " i ^ f ; b) ^ + ^ = ; c)rf(M ; A) [y = -l + 3t _£ _j_ = 1,8 ;diN-,A) = 2-, d{P ; A) = 0,8 ; A cat hai 131 canh MP va NP, khdng cdt canh MN d) Goi a va yffldn luot la goc giOa A vdi Ox \kOy,aa 36°52'; gidc ABC cd A = 60° ; b) Sut dung = -aJi^ P « 53°8' a) X - y + > b) O' = (-2 ; 2) ; = - b.hu = - C.K a) AB': b'x + ay - ab'= 0, 4^, '^ c)M = ^.ax+by + c—2iflXQ+byQ + c) A'B:bx + a'y -a'b = 0;b) AB' vd A'B c i t 3 = A: + 3y - 30 = va 2A: - 5y + 39 = — ^ — hay a'b' - ab * 0, giao dilm g b a' a) ffz < — hoac w > ; b) Tdp hop tdm ciia cac diong trrai la hai phdn cua dudng thing CO fiiucng tnnh 2A: + y - = 0, dng vdi A: < hoac x > — 2(a,-a2)Ar + 2(ftj-62)3" + ^ - ^ = 9.a)A: + = 0,5A:+12y-26 = ; b ) A r = A J ' = , 12 TT' = -j= 10 a) iE) CO hai tidu dilm ( - ; 0) ^Wz^;»Vz^Ve)a = - ^ ^ ? a'b'-ab C, I, C thing hang ; d) a'b' = 2afe a) OAB la tam giac cdn tai A, SQAB^ r 0) ; c) ( - V s ; o) va (Vs ; o ) 11 a) - V /3-3)Dc-6y-2073+^=0, M = Z V + BB^ + CC^ = , U.JB = ^ ;c)jc-2y = 0;d)(.;c-3)2 + 64 n? + 16 On tap cuoi nam ' " d) ( Q ; (B); (A); (D); (A); (D); (B); (A); (B); 10 (B); 11 (A); 12 (B); 13 (A); 14 (D); 15 (A); 16 (D); 17 (D); 18 (B); 19 (A); 20 (C); 21 (A); 22 (D); 23 (D); 24 ( Q + ^2 881 b) 12 ; b) (A: - 3) 7N2 v a (1 ; 0) ; b) (//) c6 hai tidu diem (-3 ; 0) va ; a'b'-db suy CI va CC ciing phuong, hay ba dilm Vl3 (3 a'b'-db) ta CO Xp = S + 2^I3 ,yp = + S,XQ = -2V3, = , suy M = ; d) Phdn yg = — + V3 ; e) Goi / va / ldn luot la tfch mdi vecto ABj, BC^, CAj tdng hai vecto theo quy tie hinh binh hdnh a) AM = -JB + - ^ ; CN = -JB - Jc ; 3 b) 31? = 2c2 a) A « 83°, B « 56°, C « 41° b) m^ = V46 15 /- mi, = ^ V79 V7 p S = — V ; c) r = — , R = 132 m^ = 8V7 H=iO;m),M.= ( m2 -,m •,c)Ax-2jny + m =Q\ yfm d) Dudng thing IM _ a) Tam trung dilm MN, F g thi X/ = xj Do /, / cung thudc dudng thing MN nen I = J a) F ( l ; 0), (i : A: + = ; b) A- = ( - ; OT), co vecto phdp tuyin « = (4; - 2OT) , KF cung phuang vdi n Vdy KFXIM BANG THUAT NGUT B Bdn kinh qua tieu (ddi vdi elip) 98 B^n kinh qua tieu (ddi v6i hypebol) 105 Bilu thj mdt vecto theo hai vecto khong cJjng phuong 22 Bilu tilde toa cija cae phep toan vecto 28 Bieu thiic toa dd cCia tich v6 hudng 50 Binh phuong v6 hudng eCia mot vecto 46 C6ng thufc He-rong 59 Cdng thiic hinh ehilu 49 C6ng thdc trung tuyen 58 Dudng chuan ciia parabol 110 Dudng tiem can cija hypebol 107 Dudng tron 91 Elip (dudng elip) 96 Giai tam giac 61 Gia trj luong giac ciia mot gdc 41 Gdc giCra hai vecto 44 Gdc giura hai dudng thing 88 Gdc toa 25 H DiSn tich tam giac 59 Dieu kien d l ba diem thing hang 21 Dilu kien de hai vecto cung phuong 21 Dinh cQa elip 100 Dinh cCia hypebol 106 Dinh ciia parabol 111 Djnh li cosin tam giac 53 Dinh If sin tam giac 55 D6 ddi ciia vecto 06 ddi dai so 26 Dudng cdnic 112, 114 Dudng chudn ciia elip 113 Dudng chudn ciia hypebol 113 He true toa d6 25, 26 He sd gdc ciia dudng thing 77 Hieu cCia hai vecto 15, 16 Hinh chur nhat co sd (ddi vdi elip) 100 Hinh chur nhdt cO sd (ddi vdi hypebol) 107 Hodnh 27, 40 Hypebol (dUdng hypebol) 104 K Khoang each tU mot diem de'n mot dudng thing 85 M Mdt phlng toa dp 26 133 N Nhanh cOa hypebol 106 Parabol (dudng parabol) 109, 110 Phuong tich eua mot diem ddi vdi mot dudng tron 50 Phuong trinh cac dudng phan giac 87 Tieu cU ciia elip 97 Tieu cu cOa hypebol 104 Tieu dilm cCia dudng conic 114 Tieu diem ciia elip 97 Tieu diem ciia hypebol 104 Tieu diem cOa parabol 110 Toa ciia mot diem 25, 28 Toa eCia vecto 25, 26 Toa dd ciia trpng tam tam giac 29 Phuong trinh chinh tac eCia dudng thing 82 Toa dp trung diem ciia doan thing 29 • Phuong trinh chinh tac cOa elip 98 Tdng hai vecto 9, 10 Tung dp 27, 40 Phuong trinh chfnh tac ciia hypebol 105,106 Phuong trinh chinh tac cCia parabol 110,111 Phuong trinh dUdng thing theo doan chan 77 Phuong trinh dUdng tron 91 Phuong trinh tham sd ciia dudng thing 80 Phuong trinh tiep tuyen eiia dudng tron 93 Phuong trinh tdng quat eiia dudng thing "75 Trucao 106 True be 100 True ding phuong eiia hai dudng tron 119 True ddi xumg ciia elip 100 True ddi xumg cCJa hypebol 106 True ddi xumg eiia parabol 111 True hoanh 26 Trueldn 100 True thuc 106 True toa dp 25 Quy tac ba diem 12 True tung 26 Quy t i e hinh binh hanh 12 Quy t i e ve hieu vecto 16 Vecto 3, Tam giac He-rong 60 Tam ddi xumg cCia elip 100 Tam ddi xiing ciia hypebol 106 Tam sai ciia dudng conic 114 Tam sai cCia elip 101 " Tam sai ciia hypebol 107 Tam sai ciia parabol 114 Tham sdtieu cOa parabol 110 Tfch cua mot vecto vdi mot sd 18, 19 Tfch v6 hudng ciia hai vecto 39, 44, 45 134 Vecto bang Vecto ehi phuong 80, 81 Vecto cung hudng 5, Vecto Cling phuong Vecto ddi 15, 16 Vecto-khong Vecto ngupc hudng Vecto phap tuyin 75 Vecta vudng goc 44 Vj tri tuong ddi cda hai dudng thing 78 MUC LUC Trang Chuong I-MECTO §1 Cac dinh nghia §2 Tdng ciia hai vecto §3 Hieu ciia hai vecto 15 §4 Tfch cCia mot vecto vdi mot sd 18 §5 True toa dp vd he true toa dp ' On tap chuong I 25 32 Chuang //- T(CH V HLTdNG C O A HAI VECTO VA Q N G DIJNG §1 Gia trj luong giac eCia mot goc bit ki (tU 0° den 180°) 40 §2 Tfch v6 hudng cda hai vecto 44 §3 He thufc lupng tam giac 53 6n tap chuong II 68 Chuong III - PHLTONG PHAP TOA D6 TRONG MAT PHANG §1 Phuong trinh tdng qudt ciia dudng thing 75 §2 Phuong trinh tham sd cCia dudng thing 80 §3 Khoing each va goc 85 §4 Dudng tron 91 §5 DUdng elip 96 §6 Dudng hypebol 104 §7 Dudng parabol 109 §8 Ba dudng conic 112 n tap chuong III 115 Bdi tdp on cudi ndm 126 Hudng dan - Ddp sd 129 Bing thudt ngCir 133 135 Chiu trdch nhiem xudt bdn : Chu tich HDQT kiem T6ng Giam ddc NGO TRAN AI Pho T6ng Giam ddc kiSm Tdng bifin tdp NGUYfeN QUt THAO Bien tap ldn ddu : NGUYfeN XUAN BINH - N G U Y I N TRONG THifiP Bien tap tdi bdn : PHAN THI MINH Bien tap mi thudt, kTthuat: NGUYIN NGUY£T PHl/ONG Y£N Trinh bay bia vd ve~ hinh : BUI QUANG TUAN Su!a bdn in : PHAN THI MINH NGUYET Che bdn : CONG TY CP THifT KE vA PHAT H A N H SACH GIAO DUC HINHHOCIO NANG CAO Masd:NH002T0 in 55.000 cuon, kho 17 x 24 cm In tai Cong ty Co phan In C6na Doan Viet Nam, 167 Tay SOn, Dong Oa, Ha Noi So in: 75 So XB: 01 -2010/GXB/733-1485/GD In xong va nop lUu ehilu thing nam 2010 £::.i IM V U O N G M I E N K I M Cl/ONG CHAT LUONG QUOC TE HUAN C H U G N G H O C H I MINH SACH GIAO KHOA LOP 10 LTOANHOC • DAIS61O •HiNHHOCIO TIN HOC 10 CONG NGHE 10 VAT Li 10 10 GlAO DUG CONG DAN 10 HOAHOC10 11 GlAO DUG Q U O G PHONG - A N NINH 10 SINHHOC10 12 NGOAI NGO NGli VAN 10 (tap mot, tap hai) • TieNGANHIO •TieNGPHAPIO UGH SU" 10 • TieNGNGAlO - T l t N G TRUNG Q U O G 10 OjALilO SACH GlAO KHOA LOP 10 - NANG CAO Ban Khoa hoc Ti; nhien TOAN HOC (OAI SO 10, HiNH HOC 10) • V A T U ' I O HOAHOCIO SINH HOC 10 Ban Khoa hoc Xa hoi va Nhan van NGlIf VAN 10 (tap mot, tap hai) LICH SLT 10 DjALl'lO NGOAI NGLJ (TIENG ANH 10, TIENG PHAP 10, • TIENG NGA 10, TIENG TRUNG QUOCIO) 934980110 3 Gia: 5.700d