domingo, 20 de febrero de 2011

cirunferencia

Traza las siguientes circunferencias y encuentra su ecuación en su forma general y ordinaria.
1. C(4,5)r =4



(x-h)2 + (4-k)2= r2
(x+4)2 + (y-5)2= 42
(x+4)2 + (y-5)2= 16

x2+8x+16xy2+10y25=16
x2+y2+8x+10+41-16=0
x2+y2+8x+10+25=0



2.(3,-2)r=5



(x-h)2 +(y-k)2=r2
(x+3)2+(y—2)2=52
(x+3)2+(y-2)2= 25

x2+6x+36+y2+4y+8=25
x2+y2+6x+4y+44+25=0
x2+y2+6x+64=0



4 Centro (-3,0) r=1



(x-h)2+ (y-k)2=r2
(x+3)2+ (y-0)2=12
(x+3)2+ (y-0)2=1




5. Centro (-3,0) r=1



(x-h)2+ (y-k)2=r2
(x+1)2+ (y+2)2=32
(x+1)2+ (y+2)2=9

X2+2x+1+y2+4y+4=9
x2+y2+2x+4y+1+4=0
x2+y2+2x+4y+5=0


7. Centro (-4,-2) r=2



(x-h)2+ (y-k)2=r2
(x+4)2+ (y+2)2=22
(x+4)2+ (y+2)2=4

X2+8x+16+y2+4y+4=4
x2+y2+8x+4y+16+4=0
x2+y2+8x+4y+20=0



8- c (+5,-1) r=1/2



(x-h)2+ (y-k)2=r2
(x-5)2+(y+1)2=1/22
(x-5)2+(y+1)2=1/4 ordinaria

x2-10x+25+y2+2y+1=1/4
x2+y2-10x+2y+26/1- 1/4=0
x2+y2-10x+2y + 103/4 = 0 general

26/1-1/4= 104-1/4= 103/4




9- c (2,1) r=√5


(x-h)2+ (y-k)2=r2
(x-2)2+(y-1)2=√52
(x-2)2+(y-1)2= 5 ordinaria

x²-4x+4+y²-2y+1=5
x²+y²-4x-2y+5 -5=0
x²+y²-4x-2y+0=0 general




10- c (-1/4, 7/5) r=7




(x-h)2+ (y-k)2=r2
(x+1/4)2+(y-7/5)2=72
(x+1/4)2+(y-7/5)2= 49 ordinaria

x2+2/4x+1/16+y2-14/5y+49/25=49
x2+y2+2/4x-14/5y+809/400-49/1=0
x2+y2+2/4x-14/5y-18,791/400=0 general

1/16+49/25= 25+784/400= 809/400
809/400-49/1= 809-19600/400= -10,791/400

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