C. CAU HOI VA BAITAP
§2 PHirONG TRINH Dl/CJNG TRON
3.15. a) ( x - 2 ) ^ + ( y - 3 ) ^ = 2 5 ;
c ) ( x - 2 ) 2 + ( y - 3 ) ^ = 9 ; e ) ( x - 2 ) 2 + ( y - 3 ) 2 = l .
b) (x-2)^+(y-3)^=13 ; d ) ( x - 2 ) 2 + ( y - 3 ) 2 = 4 ;
3.16. a) Phuong trinh eiia ( ' ^ ) ed dang x +y - 2ax - 2by + c = 0. Ta ed
A,B,Ce (^)
a = -3
fe = - l c = -31.
vay phuong tiinh ciia ( ' ^ ) la : x^ +y^ + 6x + 2y - 31 = 0.
<=> <
-2a-8fe + e = -17
14a-8fe + c = -65 <^ -Aa + l0b + c = -29
b) (<^) cd tam la diim (- 3 ; - 1) va cd ban kfnh bing ylâ+b^-c = JAI .
3.17. a) Ggi / (a ; fe) la tam ciia ( ' ^ ) tacd:
\l = IB^
I / G A
<=> f(a + l)^+(fe-2)^=(a + 2)^+(fe-3)^ [3a-fe + 10 = 0
r2a-2fe = -8 \a = -3
^ | 3 a - f e = -10 ^ [b = l.
Wky(^)c6tkmI(-3; 1).
h)R = IA= V(-1 + 3)^+(2-1)^ = Vs .
3.18. a ) x - y - 7 = 0 (d) hay x + y - - = 0 (d). b ) / j ^8 _13 b ) / j ^8 _13 3 ' 3 , / . f 2 U ' 7 ' 7 : ) ( ^ , ) : /^ 8 V C^J: + A2 ^ J + 13 V ^30 15 v^-"/ x + J y- 11 V 2 ^ 3 ^ 2 v35y 3.19. ( ' g ; ) : x ^ + y ^ - 8 x - 2 y + 7 = 0 Cg'2): x^ +y^ - 3 x - 7y + 12 = 0. 3.20. a) x ^ + y ^ - 4 x - 4 y - 2 = 0 ; b) x^+y^ - x + y - 4 = 0.
3.21. Phuong trinh cua ('g') cd dang (x - af +(y- af =á, ta cd
M G (^)<^ (A-ai +(2-af =â <» a -l2a + 20 = 0 <=> a = 2
a = 10.
vay cd hai dudng trdn thoa man dl bai la :
( x - 2 ) ^ + ( y - 2 ) ^ = 4 văx-10)^+(y-10)^=100. 3.22. a) Mj(l;0), M2(-3 ; 3). b) A • x - 7 y - l = 0 ; A •7x + y + 1 8 = 0. c)A 1 3.23. a) (<^) cd tam 7(3 ; -1) va cd ban kfnh B = 2, ta cd lA = V(3-l)^+(-l-3)^ = 2V5 I A > R, vky A nim ngoai C^).
b) AJ :3x + 4_v-15 = 0 ; A 2 : x - 1 = 0 .
3.24. A vudng gdc vdi d ntn phuong trinh A cd dang : x + 3y + e = 0.
C ^ ) cd tam 1(3 ; - 1) va cd ban kfnh R = VlỌ Ta cd :
AtitYrxucvdi(^)^d(I;A) = R^ ^ — j ^ = JlO « e = + 10.
VlO vay ed hai tiep tuyln thoa man dl bai la :
A, : X + 3y + 10 = 0 va A2 : x + 3y - 10 = 0.
3.25. a) C ^ ) cd tam / ( - I : 2) va cd ban kinh F = 3. Dudng thing A di qua
M(2 ; -1) va cd he sd gdc k ed phuong trinh :
y+l=k(x-2) <^ kx-y-2k-l=0.
Ta cd : A tilp xiic v(Ă^) <^ d(I, A) = R
\-k-2-2k-l\ =—^ = 3 yITVl o \k + l\ = yjk^+l <^ k^ + 2k+l=k^+l c^ k = 0.
vay ta dugc tilp tuyln Aj : y + 1 = 0.
Xet dudng thing A2di qua M(2 ; - 1 ) va vudng gdc vdi Ox, Â cd phuong trinh X - 2 = 0. Ta ed J(/, A2)= | - 1 - 2 | =3=R.
Suy ra A2 tilp xiie vdi ( ' ^ ) .
Vay qua diim M ta ve dugc hai tiep tuyln vdi ( ' ^ ) , đ la :
AJ : y + 1 = 0 va A2 : X - 2 = 0.