C. CAU HOI VA BAITAP
§2 PHUONG TRINH DUdNG TRON
CAC KEN THQC CAN NHO
1. Phuang trinh dudng trdn (h.33) • Phuong trinh dudng trdn tam I(a ; fe), ban kinh R la :
(x-af+(y-bf=P^.
• Nlu â+fê-c>0 thi phuong trinh x^+y^-2ax-2fey + c = 0 la phuong trinh ciia dudng trdn tim /(a ; fe), ban kfnh/? = va +fe - e .
• Néu â + fê - c = 0 thi chi cd mdt diim I(a ; fe) thoa man phuomg trinh
/ + y^ - 2ax - 2fey + e = 0.
• Nlu â + fê - c < 0 thi khdng cd diim M(JC ; y) nao thoa man phuong trinh .\- + y^-2ax-2by + c = 0. y , b 0 1 . M(x;y) a X Hinh 3.3
2. Phuang trinh tiep tuyen cua du&ng trdn
Ti^p tuyln tai diim MQ(XQ; y^) cua dudng trdn tam I(a ; fe) cd phuong tiinh :
(xQ-a)(x-XQ) + (yo-fe)(y-yo) = 0.
B. DANG TOAN CO BAN
VAN dE 1
Nhan dang mot phuong trinh bac hai la phuong trinh dudng trdn. Tim tarn va ban kinh dudng trdn
1. Phuang phdp
Cdch 1 : - Dua phuong trinh vl dang :
x'^ +y^ -2ax-2by + c = 0. (I) - Xet diu bilu thiic m= a +b -c.
- Nlu m > 0 thi (1) la phuong trinh dudng ti-dn tam I(a ; fe), ban kinh
/? = Vâ+fê-ẹ
Cdch 2 : - Dua phuong trinh vl dang
(x-af+(y-bf=m. (2) - Nlu m > 0 thi (2) la phuong trinh dudng trdn tam I(a ; fe), ban kfnh - Nlu m > 0 thi (2) la phuong trinh dudng trdn tam I(a ; fe), ban kfnh
R = Jm. 2. Cdc vidu
Vi du 1. Trong cac phUOng trinh sau, phuong trinh nao bi^u dien diidng trdn ? Tim tam va ban kinh neu cd :
a) x^ + y ^ - 6 x + 8y+100 = 0 (1) b) x ^ + y ^ + 4 x - 6 y - 1 2 = 0 (2) b) x ^ + y ^ + 4 x - 6 y - 1 2 = 0 (2) c) 2x^ + 2 y ^ - 4 x + 8 y - 2 = 0. (3)
GIAI
a) (I) cd dang x +y - 2ax - 2fey + e = 0, vdi a = 3, fe = - 4, e = 100.
Ta cd â +fê- e = 9 + 16 - 100 < 0.
vay (1) khdng phai la phuong trinh ciia dudng trdn.
2 2
b) (2) cd dang x +y - 2ax - 2by + e = 0, vdi a = - 2, fe = 3, c = -12. Tacd â+b^-c = 4 + 9 + 12 = 25 > 0.
vay (2) la phuong trinh cua dudng trdn tam la diim (-2 ; 3), ban kfnh bing Vâ+fê-e=5.
c) Ta cd : (3) <=> x^+y^ - 2 x + 4y - 1 = 0 » (x-1)^+(y + 2)^ =6 (adsbygoogle = window.adsbygoogle || []).push({});
<>(x-lf+(y + 2f=(j6f
vay (3) la phuong trinh ciia dudng trdn tam la diim (1 ; -2), ban kinh bing v6.
Vi du 2. Cho phuong trinh x^ + y^ - 2mx + 4my + 6m - 1 = 0. (1)