1) Mat cau c6 tam I(-2;3;-l) va tiep xiic voi duong thang , x-1 y+1 z+2 , x-1 y+1 z+2
A: = 1 1 -2 1 1 -2
2) Mat cau c6 tam I(-2;3;5) va cSt Á: ^^-^ = = ^—^ tai hai diem A, B sao cho AB = 4 sao cho AB = 4
X — 2 y — 3 z + 1
Phitaitg pliiip giai Toaii llinh liQc theo chuyen de- Nguyen Phu Khtinh, Nguyen Tat Thu
Xffigidị
1) Duong t h c i n g A di q u a A( 1; - l; - 2 ) , VTCP u = ( l ; l; - 2 ) ^.
S u y ra A i = (-3;4;]), A i A U= ( - 9 ; - 5 ; - 7 ) ;
A I A U I
Vi mat cau tiep xiic voi A nen ta c6: R = d(I, A) - N/TSS ^ V930
76 " 6 Phuongtrinh mat cau: (x + 2)^ + (y - 3)^ + ( z +1)^ = — . Phuongtrinh mat cau: (x + 2)^ + (y - 3)^ + ( z +1)^ = — .
36 2) Duong thcing A ' di qua B ( - 2 ; 3 ; l ) , VTCP u^' = (1;-1;-1)
Suy ra BI = (0; 0; 4), BI A U ' = (4; 4;0) D o d o in = d(I,Á) = Bi A u 4N/2 _ 4 V 6
' V3 " 3 Goi H la trung diem AB, ta c6 I H = h, A H = 2 S u y r a R = V h 2 + A H 2 = ^ .
^ 3 Phuong trinh mat cau: (x + if + (y - 3)^ + (z - 5)^ = — .
3
3) Duong thcing d ' qua diem N ( - 4 ; - 6 ; - 1 9 ) va c6 Uj,(3; 2; - 2 ) . V i tarn mat cau I e d nen 1(2 + t; 3 +1; - 1 + 2t).
Ta CO Mi(t; t; 21 + 2t), Ni(6 + t; 9 + t; 18 + 2t) nen N I A Uj." = (6t + 54; - 8t - 66; t +15).
Vi mat cau qua diem M va tiep xuc voi d' nen M I = d(I,d') = R. N i A U^í Do do M I = / hay . , _ V(6t + 54)^+(-8t-66)^+(t4-15)^ o 17(3t^ + 42t + 441) = lOlt^ + 1734t + 7497 o •t = o 102. • V o i t = 0 thi 1(2; 3; - 1),R = 21 nen phuong trinh mat cau
(X - 2) 2 + ( y -3) 2 + ( 2 + 1)2=441.
280
Cty TNHH MTV DWH Khang Vift
102 ^, , / 92
Voi t = — — till I - — 87 209 ^R = nen phuong t n n h m^t „ V20817 . , , - u
call f 92^ 2 ^ 87> 2 ^ 209^ X H + V + — + z + I 5 J / 5 J I 5 ) 20817 25
Vidu ,'J.4.4.Trong i<h6ng gian Oxyz cho mat cau (S) c6 phuong trinh :
||> + y 2 + z 2+ 2 x- 4 y - 6 z + m - 3 = 0 .
P Tim m de mat cau (S) tiep xuc voi mat ph5ng (a) di qua duong thSng x - 1 _ y + 1 _ z - 3