Ejercicios

Traza las siguientes circunferencias y encuentra su ecuecion de forma general y ordinaria

(x-h)² + (y-k)²=r²


(x-4)² + (y-5)²=4²

(x-4)² + (y-5)²=16



x²-8x+16+y²-10y+25=16

x²+y²-8x - 10y+41-16=0

x²+y²-8x - 10y+27=0

(x-h)² + (y-k)²=r²


(x-3)² + (y+2)²=5²

(x-3)² + (y+2)²=25



x²-6x+9+y²+4y+16=25

x²+y²-6x +4y+13-25=0

x²+y²-6x - 4y-12=0

(x-h)² + (y-k)²=r²


(x-0)² + (y+1)²=4²

(x-0)² + (y+1)²=4



x²-0x+0+y²+2y+1=4

x²+y²-0x +2y+1-4=0

x²+y²-0x +2y-3=0

(x-h)² + (y-k)²=r²

(x+3)² + (y-0)²=1²

(x+3)² + (y-0)²=1



x²+6x+9+y²-0y+0=1

x²+y²+6x -0y+9-1=0

x²+y²+6x -0y+8=0

 
 
 
 
 
(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+5-9=0

x²+y²+2x +4y-4=0

(x-h)² + (y-k)²=r²


(x+ 3/4)² + (y+2)²=6²

(x+ 3/4)² + (y+2)²=36²



x²+ 6/4x+ 9/16 +y²+4y+4=36

x²+y²+ 6/4x +4y+ 73/16- 36/1=0

x²+y²+ 6/4x + 4y- 31 7/16=0

(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+20-4=0

x²+y²+8x +4y+16=0

(x-h)² + (y-k)²=r²


(x-5)² + (y+1)²=1/2²

(x-5)² + (y+1)²= 1/4



x²-10x+25+y²+2y+1= 1/4

x²+y²-10x +2y+26- 1/4=0

x²+y²-10x +2y+253/4=0

(x-h)² + (y-k)²=r²


(x-2)² + (y-1)²=√5

(x-2)² + (y-1)²=25



x²-4x+4+y²-2y+1=25

x²+y²-4x-2y+5-25=0

x²+y²-4x -2y-20=0

(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



x²+2/4x+1/16+y²-14/5y+49/25=49

x²+y²+2/4x- 14/5y+29/400-49=0

x²+y²+2/4x- 14/5y + 391/400=0



De manera geometrica encuentra las intersecciones entre las siguientes curvas. Clasificalas como secantes, tangentes o ajenas

x²+y²-100=0 con x-y=0


x²+y²-100=0

x²+y²=100

x²+y²=10²

x²+y²-100=0 con 3/2x+y=0




x²+y²-36=0

x²+y²=36

x²+y²=6²



x=- C/A y=- C/B



x=-3/1--3-2 = -2               Y=- 3/1 =3

x²+y²-25=0 con2 x-y=0




x²+y²-100=0

x²+y²=100

x²+y²=10

x=- C/A y=- C/B



x=+4/2 =2              Y=+ 4/1 =4

x²+y²-8x+6y=0 con x-y+4=0


x²-8x y²+6y

(x-4x)² + (y+3)²=0



x²-8x+16+y²-6y+9=0

x²+y²-8x-6y+25=25

x²+y²-8x-6y+25-25=0

r=5

x=- C/A y=- C/B



x=- 4/1                y=- 4/1

x²+y²+6x-4y+9=0 con y=0


x²+6x y²-4y

(x-3)² + (y-2)²=0



x²-6x+9+y²-4y+4=0

x²+y²-6x-4y+13=4

x²+y²-6x-4y+13-4=0

r=2

x²+y²+4x-8y+4=0 con 3x-y-2=0


x²-4x y²-8y

(x+2)² + (y+4)²=0



x²+4x+4+y²-8y+16=0

x²+y²+4x+8y+20=16

x²+y²+4x+8y+20-16=0

r=5

x=- C/A y=- C/B



x=- 2/3 =0.6                   y=- 2/1 =2

2x²+2y²+8x-16y+8=0 con x-y+4=0


2x²+8x 2y²-16y

(x²+4x)² + (y²-8y)²=0



x²+8x+16x+y²-16y+64y=0

x²+y²+8x-16y+80xy=72

x²+y²+8x-16y+80xy-72=8

r=7.5

x=- C/A            y=- C/B



x=- 2/1                y=- 2/1

x²+y²-8x-8y+28=0 con x-y+4=0


x²-8x y²-8y

(x-4)² + (y+4)²=0



x²-8x+16+y²-8y+16=0

x²+y²-8x-8y+16=-12

x²+y²-8x-8y+16+12=28

r=3.4

x=- C/A            y=- C/B



x=- 1/1              y=- 1/1

x²+y²+6x-4y+4=0 con x+y-1=0


x²+6x y²-4y

(x+3)² + (y-2)²=0



x²+6x+9+y²-4y+4=0

x²+y²+6x-4y+13=9

x²+y²+6x-4y+13-9=4

r=3

x=- C/A          y=- C/B



x=+ 1/1              y=+ 1/1

x²+y²+6x+6y+9=0 con x=0


x²+6x y²+6y

(x+3)² + (y+3)²=0



x²+6x+9+y²+6y+9=0

x²+y²+6x+6y+18=9

x²+y²+6x+6y+18-9=9

r=3