e <1 x2 a2 +y2 b2 = 1 a &gt

Lyc´ee Pierre de Fermat Formulaire

MPSI 1 Coniques

Ellipses :0< e <1

x² a² +y²

b² = 1

a > b a < b

c=p a²−b²

e= c a

c=p b²−a²

e= c b

O

O a

-a

b

-b x=−a²

c D^′

x= a² c D

(c,0) F

b b

F^′ (−c,0)

(0, c) F ^b

(0,−c) F^′b

a -a

b

-b

y= b² c D

y=−b² D^′ c

Paraboles : e= 1 y²= 2px

O O b

F p

2,0

−p 2,0

D x=−p

2

b

y²=−2px

b

D

F

−p 2,0

b

p 2,0 x=p 2

Hyperboles :e >1 x²

a² −y² b² = 1 c=p

a²+b² e= c

a

O

-a O a

y = b ax y=−b

ax

b(c,0)

F

b(−c,0)

F^′

x=a² c D x=−a²

c D^′

−x² a² +y²

b² = 1 c=p

a²+b² e= c

b b

-b y= b

ax y=−b

ax

b(0, c) F

b(0,−c) F^′

y= b² D c

y=−b² c D^′

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