Matematica

COLEGIO ANTIGUA
PROF. DIMIDRI
4TO. TURISMO

GRAFICAS

JACKELIN JOHANA MERIDA JUAREZ
CLAVE: 18

ANTIGUA GUATEMALA 7 DE OCTUBRE DEL 2010


1)
x²+y²=(√5)²
x²+y²=5



2)centro (0,0) r=√ 7
x²+y²=(2√7)²
x²+y²=28

3)Centro (0,0) r=√2
x²+y²=(√2)²
x²+y²=2

4)Centro (0,0) r=√3
x²+y²=(√3)²
x²+y²=3



5)centro (0,0) r=3√2
x²+y²=(3√2)²
x²+y²=45

6)Centro (0,0)r=√6
x²+y²=(√6)²
x²+y²=6

7)Centro (0,0) r=3√2
x²+y²=(3√2)²
x²+y²=18

8)Centro (-1,3) r=√2
(x-(-1))²+ (y-3)²= (√2)²
(x+1)²+(y-3)²=2

9)centro (5,-2) r=√3
(x-5)²+ (y-(-2))²= (√3)²
(x-5)²+(y+2)²=3

10)Centro (-2,-6) r= 2√3
(x-(-2))² + (y-(-6))² = (2√3)²
(x+2)² + (y+6)² = 12

11)Centro (-3,7) r= √7
(x-(-3))² + (y-7) = (√7)²
(x+3)² + (y-7)² = 712)Centro (5,2) r= 3√2
(x-5)² + (y-2)² = (3√2)²
(x-5)² + (y-2)² = 18

13)Centro (7,-3) r= 3√2
(x-7)² + (y-(-3))² = (3√2)²
(x-7)² + (y+3)² = 18

14)centro (-1,-8) r= 4√2
(x-(-1))² + (y-(-8))²= (4√2)²
(x+1)² + (y+8)² = 32
²

15)centro (-1,7) r = 2√2
(x-(-1))² + (y-7)²= (2√2)²
(x+1)² + (y-7)²= 8

16)Centro (-3,6) r= √3
(x-(-3))²+(y-6)²= (√3)²
(x+3)²+(y-6)²= 3

17Centro (0,7) r= √2
(x-0)²+ (y-7)² = (√2)²
(x-0)²+ (y-7)² = 2

18)Centro (-1,0) r= √4
(x-(-1))² + (y-0)² = (√4)²
(x+1)² + (y-0)² = 4

19)Centro (3,6) r= 3√4
(x-3)² + (y-6)² = (3√4)²
(x-3)² + (y-6)² = 36

Determinación de la forma estándar por la compleción de cuadrados

20)centro (-4,3) r= √40
x²+8x+y²-6y=15
x²+8x+ 16+y²-6y+9=15+16+9(x+4)²+(y-3)² =40

21)Centro (-3,2) r= √28
x²+6x+y²-4y= 15
x²+6x+9+y²-4y+4= 15+9+4
(x+3)²+(y-2)²= 28

22)Centro (4,-1) r= √4
x²-8x+y²+2y= -13
x²-8x+16+y²+2y+1= -13+16+1
(x-4)²+ (y+1)²= 4

23)Centro (-3,-2) r= √1
x²+6x+y²+4y=-12
x²+6x+9+y²+4y+2=-12+9+2
(x+3)²+(y+4)² =1

24)Centro (0,-5) r= √4
x²-4x+y²= 0
x²-4x+4+y²= 0+4
(x-2)²+y²=4

25)Centro (0,-5) r= √100
x²+y²+10y+25= 75+25x²+(y+5)²= 100

Elipses

26) x2 + y2 = 1
a= 2
b= 1
c=√4-1
c√3= 1.73


27) x2/1 + y2/4 = 1
X2/1 + y2/2 = 1

A=2
B= 1
C=√4-1
C=√3= 1.43


28) 16x2/144 + 9y2/144 = 144/144
X2/9 + y2/16 = 1
X2/3+ y2/4 = 1
A= 4
B= 3
C=√16-9
C=√7= 2.64

29) 2x2/6 + 3y2/6 = 6/6
X2/3 + y2/2 = 1
X2/(√3)2 + y2/(√2)2 = 1
A= √3= 1.43
B= √2= 1.41
C=√3-2
C=√1 = 1

Completar cuadrados para encontra la forma estándar.

30) x2/9 + y2/1 = 1x2/3 + y2/1 = 1
a= 3
b= 1
c= √9-1
c= √8 = 1


31) x2/1 + y2/4 = 1
x2/1 + y2/4 = 1
x2/1 + y2/2 = 1
a= 2
b= 1
c= √4-1
c= √3 = 1.43


32) 5x2/35 + 7y2/35 = 35/35
X2/7 + y2/5 = 1X2/(√7)2 + y2(√5)2 = 1
A= 7 = 2.64
B= 5 = 2.23

33) (x-1)2/1 + (y-2)2/4 = 1
(x-1)2/1 + (y-2)2/2 = 1
A= 2
B= 1
C= √2-1
C= √1 = 1

34) (x-2)2/9 + (y+4)2/4 = 1
(x-2)2/3 + (y+4)2/2 = 1
A= 3
B= 2
C= √9-4
C= √5 = 2.2335)x2+2y2-10x+8y+29= 0
x2-10x+2y2+8y= -29
x2-10+25+2(y2+4y+4)=-29+25+2*4
(x-5)2/4 + 2(y+2)2/4= 4/4
(x-5)2/4 + (y+2)2/2 = 1
(x-5)2/4 + (y+2)2/(√2)2 = 1
A= 2
B= √2 = 1.41
C=√4-2
C=√2 = 1.41

36) 9x2+4y2+54x-8y+49 = 0
9x2+54x+4y2-8y = -49...