1 - ^ , 4 5 j , 4 5 j ^~5 130 ^ „ 7130 => AB = 9 3 = 30=>AB = >/30.
Vi dxjL 1.4.20. Trong m^t phang vdi h§ tpa dp Oxy, hay viet phuong trinh
chinh tSc cua eh'p (E) biet rS: so cua (E) CO chu v i b5ng 20.
chiiUi tSc cua eh'p (E) biet rSng (E) c6 tarn sai bang — va hirih chii nhat co 3
JCffigidi
x^
Gpi phuong trirUi chinh tSc a i a elip (E) la: — + ^ = 1, v o i a > b > 0.
Tu- gia t^"*'^* phuong trinh:
c ^ 7 1
a 3 (I V
2(2a + 2b) = 20
Giai he tren, ta tim dugc: a = 3 va b = 2 .
x2 y2
phuong trinh chinh tac cua ( E ) la: + — = 1 • '•1 ^'(. il
Vidu 1.4.21. Tron^ mat phcing Oxy cho Elip + ^ = • '^'^^ phuong
trinh hypebol (H) c6 hai duong tiem can y = ±2x va c6 hai tieu diem la hai tieu diem cua (E).
Gia su hypebol (H) c6 dang :
Xffi giaị
y ^
n2
= 1
'.'4 i'Vv', ••
Vi (H) CO hai t i f m can y = ±2x nen ta c6: — = 2 => n = 2 m . i 4 -nA
m Doi voi elip ta c6: c^ = â - b^ = 12 - 2 = 10.
Theo gia thiét thi tieu diem ciia Hypebol cung la cua elip nen: ^ , ,
c^ = m^ + n^ o 10 = + {Imf = 5m^ o m^ = 2,n^ = 8
x^ y2
Phuong trinh hypebol (H) la: — - ^ = 1 .
2 8
Vidu Viet phuong trinh chinh tSc cua hypebol (H), biet:
1) (H) d i qua hai diem M(V2;2V2) va N ( - 1 ; - V 3 ) ,
2) (H) d i qua E ( - 2 ; 1 ) va goc giua hai duong tiem can bang 60" .
Xgigidị
Gia su (H): x2 y 2 _ â b^ = 1.
1) Do (H) di qua hai diem u(4i;l4l) va N(-1;->/3
2 8 5 . •0 '•• nen ta c6 h^: â \ ^-4 = 1 â b^ 5:
Phutmg phdp gidi Todn Hinh HQC theo chuyen de- Nguyen Phu Khanh, Nguyen Tat Thu
^ 2 2
Vay phuong trinh (H) la : ^ ~ ^ = ^ 5
2) V i E ( - 2 ; l ) e ( H ) n e n t a c o 4-^ = 1 (1) a b
Phuong trinh hai duong tiem can la:
Aj : y = - x hay b x - a y = 0 va A2 : y = - - x hay bx + ay = 0.
a a
Cty TNHH MTV DWH Khang Viet
d ( F ; A ) = P - 1 2
= 2N/2 suy ra p = 16 hoac p = 32. ,
V i goc giua hai d u o n g tiem can bang 60*^ nen cos60" = b ^ - a ^
b 2 - a 2
ay phuong trinh cua (P): y^ = 32x hoac y^ = 64x
2) Ta thay (P) luon cat duong thang A tai goc toa do, gia su B = O va A la giao diem con laị
Vi A e A=> A ( a; 3 a ) .
Matkhac A B = 4V2=> Va^T9â = 4V2<:>a2 =-5^=>a = ±
D + a Hay - = Hay - = 2 b 2 - 2 » 2 b^-â .2 0-2 2 2 ( b ^ -2 ( b ^ - 2{b^ - 2 2 x y =1 11 11 3' ,2 . 2 . , 2 , 7 - 2 , . 2 , b2=3a2 a2=3b2 Ml V i
Suy ra p h u o n g trinh hypebol la (H):
• Voi â = 3b2 thay vao (1) dugc â = 1, b^ = -
3
Suy ra p h u o n g trinh hypebol la (H): — - i — = 1
3
Vay C O C O hai hypebol thoa man c6 phuong trinh la:
y ' ^ x2 y2 ^
— - — = 1 va — = 1.
11 11 1 1
W d u 1.4.2,1 Viet phuang trinh chinh t3c ciia Parabol (P), biet:
1) Khoang each t u tieu diem F den duong th^ng A : x + y - 1 2 = 0 bang 2V2 . 2) (P) cat d u o n g thang A : 3x - y = 0 tai 2 diem A, B sao cho A B = 4>/2 . 2) (P) cat d u o n g thang A : 3x - y = 0 tai 2 diem A, B sao cho A B = 4>/2 .
Xgigidị