Huang in PHirONG PHAP TOA DO TRONG MAT PHANG A CAC KIEN THlfCCO BAN VADE BAI §1 Phaong trinh tdng quat cua dudng thang I - CAC KIEN T H Q C CO BAN • Phuong trinh tdng qudt cua dudng thdng co dang ax + by + c = t) ia +b ^ n =ia;b) la mgt vecta phdp tuyen Ddc biet: - Khi b = thi dudng thing ax + c = song song hodc triing vdi Oy (h 19a); - Khi a = thi dudng thdng by + c = song song hodc triing vdi Ox (h 19b); - Khi c = thi dudng thdng ax + by = di qua gdc toq (h 19c) • Dudng thing di qua M(xo ; >'o) vd nhan n=ia; b) lam vecta phdp tuyen co phuang trinh a(x-Xo)+ biy-y^) =0 Dudng thing cdt true Ox tai Aia ; 0) vd Oy tqi BiO ; b) ia va b khdc 0) co X y a b phuong trinh theo doan chdn —\- — = I (h 80) • Phuang trinh dudng thing theo he sd goc co dqng y = kx + b, k = tana vdi a la goc gida tia Mt iphdn cua dudng thing ndm phia tren Ox) vditiaMxih 81) • Dudng thing qua M(xo; yo) vd co he sdgoc la k thi co phuang trinh: y-yQ y^ y' o X kix-XQ) y^ y^ i = O O a) b) Hinh 79 O c) Hinh 80 Hinh 81 99 Vi tri tuang ddi ciia hai dudng thing Cho hai dudng thdng Aj : a^x + b^y + Cj = vd A2 : a2X + b2y + C2 = Ddt D= a, ^1 D,= «2 ^2 A^cdt bl ci Cj ^2 ^2 A2 .-2)' = ; d)x^ + / - IOx- 10^ = 55 ; h) ix - 5)h iy +if =15; e) x^ + y^ + 8x - 6j + = ; c) x^ + y^-6x-4y = 36; f)x^ + / + 4x+ I0y+ 15 = 43 Vilt phuong trinh dudng trdn dudng kfnh AB eac trudng hgp sau a) A(7 ; - ) ; 5( ; 7) ; b) A(-3 ; 2); 5(7 ; -4) 44 Vilt phuong trinh dudng trdn ngoai tid'p tam giac ABC bilt A = (1 ; 3), = (5 ; 6), C = (7;0) 45 Vilt phuang trinh dudng trdn ndi tilp tam giac ABC bilt phuong trinh cac canh A5 : 3x + 4j - = ; AC : 4x + 3y - = ; BC •.y = 46 Bien ludn theo m vi tri tuong ddi cua dudng thing A^ : x - my + 2m + = va dudng trdn i% : x^ + y^ + 2x - 2y-2 = 47 Cho ba dilm A(-l; 0), 5(2 ; 4), C(4 ; 1) a) Chiing minh ring tdp hgp cdc dilm M thoa man 3MA^ + MB^ = 2MC^ la mdt dudng trdn i9p) Tim toa dd tdm vd tfnh bdn kfnh cua (*^ 107 b) Mdt dudng thing A thay ddi di qua A cdt ( ^ tai M vd N Hay vilt phuong trinh cua A cho doan MN ngan nhdt 48 Vilt phuong trinh dudng trdn tid'p xuc vdi cae true toa vd a)DiquaA(2;-l) ; b) Cd tdm thudc dudng thing 3x - 5^ - = 49 Vilt phuong trinh dudng trdn tiep xuc vdi true hodnh tai dilm A(6 ; 0) va di qua dilm 5(9 ; 9) 50 Vilt phuang trinh dudng trdn di qua hai dilm A(-l ; 0), 5(1 ; 2) va tilp xuc vdi dudng thing x-y - I =0 51 Vie't phuang trinh dudng thing A tid'p xiic vdi dudng trdn ( ^ tai A e i% mdi trudng hgp sau rdi sau dd ve A vd (*^ trdn cung he true toa dd a) i%:x^ + y'^ = 25, A(3 ; ) ; d) ("^ : x^ + / = 80 , A(-4 ; - ) ; b) ( ' ^ : x^ + / = 100, A(-8 ; 6); e) ( ' ^ : (x - 3)^ + (y + 4)2 = 169, A(8 ;-16); c) ( ' ^ : x^ + 3;^ = 50, A(5 ;-5); f)i% :ix + 5f+ iy- 9f = 289, A(-13 ; -6) 52 Cho dudng trdn i9^ : ix - af + iy - bf = R^ vk diim M^ix^ ; JQ) e i% Chiing minh ring tilp tuyd'n A eua dudng trdn ( ^ tai MQ ed phuang trinh : (XQ - a)(x - a) + (3'o - b)iy -b) = R 53 Cho dudng trdn ( ^ :x +y - x + 63' + = 0va dudng thing d : 2x + y - = Viet phuang trinh tilp tuyin A eua (©), bie't A song song vdi d ; T m toa dd tid'p diem 54 Cho dudng trdn i% : x^ + / - 6x + 2^ + = vd dilm A(l ; 3) a) Chifng minh ring A d ngodi dudng trdn ; b) Vilt phuang trinh tid'p tuyd'n cua (*^ ke tir A ; c) Ggi Fl, r2 la cdc tilp dilm d cdu b), tfnh didn tfch tam gidc AT{r2 55 Cho dudng trdn i% cd phuong trinh x^ + y^ + 4x + 4y -17 = Vilt phuang trinh tilp tuyin A ciia ( ^ mdi trudng hgp sau a) A tilp xiic vdi i% tai M(2 ; 1); b) A vudng gdc vdi dudng thing d : 3x - 43" +1 = ; c) A di qua A(2 ; 6) 108 ... = l + 2t a) Al :