14
 I R 2 l  F  l  P F  l  l F  F  l directriz vertice foco eje x Parabola F  y  F  (0,c)

conicas.pdf

Embed Size (px)

Citation preview

  • "!$#&%(')+*-,

    IR2

    .

    0/ )*)21**43658785:9$;=5@?BADCFEG5

    l H;=

  • 3m};2JKBwYv 8%8;: 8;F D2Bw |8;:f F 5 8Vv 0 58vFw x:Qy@8%F 5 y=w 248Vv K42Bw 5 y@8H7J8;2

    y = c -C:K4D:Kv 8"7 F 5 8Vv 0 58vFw x:Qy@8%F 5z 562D{6EDF 5nv D:3m};2JKBwYv 8 c CDLT

  • ba

    Foco Foco

    Elipse

    .

    0/ )*)21* 365878L:9

    c, a IR+ EG5TR AN9$WF;KA a < c CDLT

  • M

    u

    5'8Vv 0 58vFw x: y@8=0(: 5\w z>};24EDF 5rv D:$ D=v D 7

    F1 = (c, 0) ~ F2 = (c, 0) ~ 7J8;Grw 8c 8"7 a ~ b 8"7

    x2

    a2 y

    2

    b2= 1.

    d #F*') # *-)a! *)

    ** piCBLTz D2 F DK 56:K4D

    mn(5) = 1-

    &

    2' CF-v D:m 0(: K4D

    68"7 KD{ 58v D6K 58y@D 7J0\z8;2Bw D2'8 w := 8;2Bw D24G%8;:K48 ~8"7':(D 3 58v)( DK&zD2'K 56:K4D 8)*=w 7 K48

    7J0\z(248;G%DB89( :-, G%D -%.-y@8;Gd{7

    sup(6) =26~

    inf(6) = 2-CA D2HD6K 24D F 58y@DK v DG%D56G E D 7

    z8;2JK48;:(8Vv 8;:56Fav D:m 0(: K4Dkv D8w :KvFwYy@8;:v D: 8;F Gd{3*=w G%Dr~ 8;F G/( :\w G%D%248"7cz 8Vv KBw 3 56G%8;: K48-

  • *AGI?BAN9AF

  • ,

    *n5TROR 5T? AFRKsTtF?NEPM2CDA

    AFR:hNLVCDL

    H

    R L:9 CBA?cL:9 78A(R 5:99NM m;=M2AF

  • ,,

    &

    O2'- 8"5

    y(x) = x2 + 2x + 1 = (x + 1)2,8 : K4D:Kv 8"7I8;Ffv 8;24D'8"7

    x = 1 ~ 8;F 38};2JKBwYv 8

  • ,

    3m};2JKBwYv 8'7J8'DE@KBw 8;:(86y@8

    y(x) = 2x + 1 = 0 = x = 12.

    K42 5d D24GH5ky@8 56F F 562 8;F38};2JKBwYv 8n~ 5 7J0

    368 '8;F& D\v D 8"7 248Vy@0KvFw 8;:Ky@D F 5 8Vv 0 58vFw x: 5 0(: 5 8)*=z(248"7cw x:Zy@8'F 5d D24GH5

    4c(y y0) = (x x0)2 - C:8"7 K48lv;57JDK

    4( 14)(y 3

    4) = (x + 1

    2)2\zD2IK 56:K4DH8;F 38};2JKBwYv 8

  • ,"O

    !#")21%$

    u

    5 8Vv 0 58vFw x:gy@8H0(: 5@vFw 2Dv 0(:= 8;248;:KvFw 5 8"7

    (x x0)2 + (y y0)2 = r2 - A D20'

    (x 1)2 + (y + 1)2 = 16 @248z(248"7J8;:K 5 0(: 5rvFw 2Dv 0(:= 8;248;:KvFw 56y@8

  • ,

    r = 12

    ~$v 8;: K424D%8;Ffz@0(: K4D

    (0, 0)-

    xy

    4

    2

    20

    -2

    0

    -4

    -2

    (5)

    y

    x

    0,6

    0,6

    0,4

    0,2

    0,40

    -0,2

    0,2

    -0,4

    -0,6

    0-0,2-0,4-0,6

    (6)

    * + n5TROR 5T?nAFR CBAF

  • , >

    &

    ,'

    u

    5 8Vv 0 58vFw x:H248Vy@0KvFwYy(5=8"7

    x2

    22+ y2 = 1

    - A D21K 56:K4DK 7J8 K42 5 K 5y@8 0(: 5 8;F w z 7J8oy@8ov 8;: K424D 8;F

    (0, 0)~ 7J8;Grw 8c 8"7

    a = 2~

    b = 1-

    &

    0'

    u

    5 8v 0 58vFw x: 248Vy@0KvFwYy(5H8"7

    (x 1)232

    + y2 = 1-A D2 K 56: K4DK7J8 K42 5 K 5ky@80(: 5H8;F w z 7J86y@86v 8;: K424D

    8;F

    (1, 0)~ 7J8;Grw 8c 8"7

    a = 3~

    b = 1-

    x

    20-2-4-6

    (3)y

    1,510,50-0,5-1-1,5

    4

    0,8

    3,8

    3,6

    0,40-0,4-0,8

    (4)

    y

    4,4

    x

    4,2

    &

    O2'

    u

    5'8Vv 0 58vFw x: 248Vy@0KvFwYy(5'8"7

    (x + 2)2

    (15)2

    +y2

    (

    15/8)2= 1

    -(A D2IK 56: K4DK(7J8

  • ,

    &

    >0'

    u

    5'8Vv 0 58vFw x: 248Vy@0KvFwYy(5'8;7

    (x + 1)2

    (1/7)2

    +(y 1)2(

    14/3)2= 1

    -@A D2IK 56: K4DK(7J8

  • ,

    y

    x

    4

    4

    2

    02

    -2

    -4

    0-2-4

    (3) (4)

    y

    10

    8

    6

    4

    2

    0

    x-2

    -4

    6420-2-4

    &

    '

    u

    58Vv 0 58vFw x: 248Vy@0KvFwYy(56y@8 F 5 \w z};24E DF 5 8;: 8"7 K48lv;57JD8"7

    (x 1)29

    (y 3)2

    16= 1

    =zD21K 56:K4D

    F 57

  • ,"M

    *i;KtEPM I\L$78ArCF;=?NsT5d?cAGI?BAN9AF0'

    u

    5rv 0(243 5

    2(x + 1)2 + 4(y 1)2 = 16 248z(248"7J8;: K 50(: 5%8 FYw z 7J8ly@8=8Vv 0 58vFw x: 248Vy@0KvFwYy(5

    (x + 1)2

    22

    +(y 1)2

    2= 1.

    &

    2'

    u

    5rv 0(243 5 3x2 + y2 6x = 0 248z(248"7J8;: K 50(: 5\w z>};24EDF 56y@8=8Vv 0 58vFw x: 248Vy@0KvFwYy(5

    (x + 1)2 y2

    3= 1.