7/25/2019 algebra trigonometria y geometia analitica momento # 6.docx

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TRABAJO COLABORATIVO # 6ALGEBRA

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNADINGENERIA DE ALIMENTOS

2016

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TRABAJO COLABARATIVO #6

Resolver c! "o !e los s$%"$e&es 'ro(le)s 'ro'"es&os*

1+ De)os&rr ,"e* 4x2+9y2+24x+36y+36 - 0 es l ec"c$. !e " el$'se /

!e&er)$e*

+ Ce&ro(+ ocosc+ Vr&$ces

4x2+9y2+24x+36y+36=0

4x2+24x+36y+9y2=36

4 (x2+6x )+9 (y2+4y )=36

(x2+6x)+94

(y2+4y )=9

1

9(x2+6x )+ 1

4(y2+4y )=1

1

9(x2+6x+9)+ 1

4(y2+4 y )=1+ 1

4(9)

y+22

=1+1

9 (9 )+1

4 (4)

x+32+1

4

1

9

y+22=1

x+32+1

4

1

9

7/25/2019 algebra trigonometria y geometia analitica momento # 6.docx

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x+32

y+22

(x(3 ))

32 +

(y (2 ))

22 =1

(h ,k)= (3,2 ) ,a=3,b=2

Ce&ro* (3,2)

ocos* 4x2+9y 2+24x+36y+36=0

x(3)2

y(2)2

(h ,k)= (3,2 )a=3,b=2

3,c ,2(3,c ,2 ) ,

llr C*

c=3222

c=94

c=5

Foco: (3+5 ,3) ,(3,5 ,2)

Ver&$ces* (h+a , k)(h ,a , k)

4x2+9y2+24x+36y+36=0

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x(3)2

y(2)2

(h , k)= (3,2 )a=3,b=2

(h+a ,k) (ha ,k)

3,3,2(3,+3,2 ) ,

(0,2)(6,2)

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2+ De l s$%"$e&e ec"c$. c.$c !e l el$'se3 &rs4or)r l ec"c$.*

5

xc 2+y2

x+c2+y2

E l ec"c$.*x

2

a2

y2

b2=1

+ De)os&rr ,"e l ec"c$.* 9x24 y254x+8y+113=0 re'rese& "

7$'r(ol+ De&er)$e*

+ Ce&ro(+ ocosc+ Vr&$ces

9x24 y254x+8y+113=0

9x254 s+8y4y 3=113

(x26x )4 (y22y )=1139

1

4 (x2

6x+9 )1

9 (y2

2y )=113

9 +1

4 (9)

x321

9(y22y+1 )=113

36+1

4(9 )

1

9(1)

1

4

y12=1

x321

9

14

x3

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y12

Hiperbola :

Ce&ro* (3,1)

oco* (h ,k)= (3,1 )a=3,b=2

(3,1+c ) ,(3,1,c )

Ver&$ces :h ,k+a (h ,ka)

9x24 y254x+8y+113=0

y1 2

(h ,k)= (3,1 )a=3,b=2

(h , k ,+a ) , (h , k ,a )=(3,1+3 ) ,(3,1,3)

(3,4 ) ,(3,2)

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8+ De!"c$r l ec"c$. !e l 7$'r(ol*

x2

a2y

2

b2=1

A 'r&$r !e l ec"c$.

xc 2+y2

x+c2+y2

9+ De)os&rr ,"e l ec"c$. x2+y210x+18=0 es " c$rc"4erec$+

De&er)$r*x

2+y210x+18=0

x2+y210x=18

x210x+y2=18

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x

( 210x )+y2=18

(x210x+25 )+y2=18+25

x

:or &&o3 l ec"c$. re!"c$! !e l c$rc"4erec$ es*

x

+ Ce&ro

(a , b )=(5,0)

(+ R!$o

r2=7

r2=7

r=7

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6+ De)os&rr ,"e l ec"c$.* 4x 2

20x 24y+97=0re'rese& " 'r;(ol+

De&er)$e*

+ Vr&$ce(+ ococ+ D$rec&r$