conique cours

3 ﻴﺤﻟ ﺪﻤ ﻣﺤ 2 . ب. ع. رﻳ . - 1 - ت ﻴﻃوﺮﺨﻤﻟ ﺔﻴﻧ ﺜﻟ ﺔﺟرﺪﻟ ﻦ ﻣ ت ﻴﻨﻨﺤﻤﻟ ل ﺜ ﻣ1 : ﺳﻷ ﺮﻴﻴﻐ ﺑﺘ ﻢﻟﻤﻌﻠ ﺮﻴﻴﻐ ﺗ ﻰ ﻋﻠ ﺪﻤﺘ ﺗﻌ ﻰﻟﻷو ﺔﻘﺮﻳﻄﻟ ﻢﻈﻨﻤ ﻣ ﺪﻣﺎﻌﺘ ﻣ ﻢﻠﻌ ﻣ ﻰﻟ إ بﻮﺴﻨﻤﻟ ا ىﻮﺘﺴﻤﻟ ا ﻲ ﻓ( ) , , O i j ﺔﻮﻋﻤﻤﺠﻟ ا ﺮﺒﺘﻌ ﻧ : ( ) ( ) { } 2 2 , / 5 5 6 8 0 E M x y x y xy = ∈ + + − = P . ﻲﻬﺠﺘﻤﻟ ا ىﻮﺘﺴﻤﻟ ا ﻲ ﻓ2 V ﻦﻴﺘﻬﺠﺘﻤﻟ ا ﺘﺒﺮﻌ ﻧ : 2 2 2 2 u i j = + و 2 2 2 2 v i j = − + . 1 . ﻨﻤﻨﺤﻠ ﻟ ﺗﻴﺔرﺎﻜﻳ د ﺔﻟدﺎﻌ ﻣ دﺪ ﺣ( ) E ﻠﻌﻤﻟ ا ﻲ ﻓ ( ) , , O u v ﻰﻨﻨﺤﻤﻟ ا ﺔﻌﻴﺒ ﻃ ﺞﺘﻨﺘﺳ ا ﻢ ﺛ ( ) E . 2 . ﻨﺤﻨﻤﻟ ا ﺊﺸﻧ أ( ) E ﻠﻌﻤﻟ ا ﻲ ﻓ ( ) ,, O i j . ﻞﺤﻟ : ﺮﻴآ ﺗﺬ : نﺎ آ ذا إ( ) , i j و ( ) , u v ﺚﻴ ﺣ ﺎنﻤﻈﻨﻤ ﻣ ناﺪﻣﺎﻌﺘ ﻣ نﺎﺳﺎ ﺳ : ( ) [ ] , 2 i u θ π ≡ و 0 2 π θ < < نﺈ ﻓ : ( ) ( ) cos sin u i j θ θ = + و ( ) ( ) sin cos v i j θ θ = − + . ﺪﻳﻨﺎ ﻟ ﺜﺎلﻤﻟ ا ﻲ ﻓ : ( ) 2 cos sin 4 4 2 u i j i j π π ⎛ ⎞ ⎛ ⎞ = + = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ و ( ) 2 sin cos 4 4 2 v i j i j π π ⎛ ⎞ ⎛ ⎞ = − + = − + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ . رﺘﻴﺎﺧ ا ﻢﺘ ﻳ 4 π θ = ن ﻮ ﻜ ﺗ ﺚﻴﺤ ﺑ ﺎدﻟ ﻌ( ) E ﺤﻟ ا ﻰﻠ ﻋ ﺔﻳﻮﺘﺤ ﻣ ﻴﺮ ﻏ xy . 1 . ﺘﺒﻌ ﻧ M ﻮﺘﺴﻤﻟ اﻦ ﻣ ﺔﻄﻘ ﻧ P ﺚﻴﺤ ﺑ : ( ) , x y ﻄﻘﻨﻟ ا ﻲﺘﻴﺛﺪاﺣ إ جو ز ﻮ ﻩ M ﺴﻨﻟﺎ ﺑ ﻠﻌﻤﻠ ﻟ ﺔ( ) , , O i j ( ) , X Y ﻨﻘﻄﻟ ا ﻲﺘﻴﺛﺪاﺣ إ جو ز ﻮ ﻩ M ﻠﻌﻤﻠ ﻟ ﺔﺒﺴﻨﻟﺎ ﺑ ( ) , , O u v . ﺎﻨﻳﺪ ﻟ : ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 OM x i y j X u Y v x i y j X i j Y i j x X Y y X Y = + = + ⇔ + = + + − + ⎧ ⎪ = − ⎪ ⇔ ⎨ ⎪ = + ⎪ ⎩ نﺈ ﻓ ﻪﻨﻣ و : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 5 6 8 0 5 5 6 8 0 2 2 2 5 2 5 2 6 16 0 16 4 16 0 1 1 2 M E x y xy X Y X Y X Y X Y X X Y Y X X Y Y X Y X Y X Y ∈ ⇔ + + − = ⇔ − + + + − + − = ⇔ − + + + + + − − = ⇔ + − = ⇔ + = نذ إ ( ) E ﺰﻩآﺮ ﻣ ﺞﻴﻴﻠﻠﻩ إ( ) 0, 0 O ﻢﻠﻌﻤﻠ ﻟ ﺔﺒﻨﺴﻟ ﺑﺎ ﻪ ﺳ و ؤ ر و ( ) , , O u v ﻲ ﻩ : ( ) 1 , 0 A و ( ) 1 , 0 A ′ − و ( ) 0, 2 B و ( ) 0, 2 B ′ − . ﺎﻨﻳﺪ ﻟ : 1 a = و 2 b = . ن أﺎﻤ ﺑa b < نﺈ ﻓ : 2 2 2 2 2 1 3 c b a = − = − = ﻴﻴﻠﻠﻩﻹ ا ﻲﺗرﺆ ﺑ نﺈ ﻓ ﻨﻪﻣ و ( ) E ﻠﻤﻌﻠ ﻟ ﺔﺒﺴﻨﻟﺎ ﺑ ( ) , , O u v ﺎﻤ ﻩ ( ) 0, 3 F و ( ) 0 3 F ′ − . ﺎﻤ ﻩ ﻴﻼﻩﻟد و: ( ) 4 3 : 3 D Y = و ( ) 4 3 : 3 D Y ′ = − . θ

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cours math conique

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= + + + + + + Y X Y X Y X Y X = + + + + +X Y YX Y X YX Y X0 61 6 2 5 2 52 2 2 2 2 2) ( ) ( ) ( :

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