1- C (4,5) r=4
(x-h)²+ (y-k)²=r²
(x-4)²+(y-5)²=4²
(x-4)²+(y-5)²=16 ordinaria
x²-8x+16+y²-10y+25=16
x²+y²-8x-10y+41-16=0
x²+y²-8x-10y+25=0 general
2- c(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 ordinaria
x²-6x+9+y²+4y+4=25
x²+y²-6x+4y+13-25=0
x²+y²-6x+4y-12=0 general
3- c (0, -1) r=2
(x-h)²+ (y-k)²=r²
(x-0)²+(y+1)²=2²
(x-0)²+(y+1)²=4 ordinaria
x²+0+y²+2y+1=4
x²+y²+2y+1-4=0
x²+y²+2y-3=0 general
4- c (-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 ordinaria
x²+6x+9+y²+0=1
x²+y²+6x+9-1=0
x²+y²+6x+8=0 general
5- c (-1,-2) r=3
(x-h)²+ (y-k)²=r²
(x+1)²+(y+2)²=3²
(x+1)²+(y+2)²=9 ordinaria
x²+2x+1+y²+4y+4=9
x²+y²+2x+4y+5-9=0
x²+y²+2x+4y-4=0 general
6- c (-3/4, -2) r=6
(x-h)²+ (y-k)²=r²
(x+3/4)²+(y+2)²=6²
(x+3/4)²+(y+2)²=36 ordinaria
x²+6/4x+9/16+y²+4y+4=36
x²+y²+6/4x+4y+73/16-36/1=0
x²+y²+6/4x+4y-503/16=0 general
9/16+4/1= 9+64/16= 73/16
73/16-36/1= 73-576/16= -503/16
7- c (-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 ordinaria
x²+8x+16+y²+4y+4=4
x²+y²+8x+4y+20-4=0
x²+y²+8x+4y+16=0 general
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
De manera geométrica encuentra las intersecciones entre las siguientes curvas. Clasifícalas además como secantes, tangentes y ajenas.
1- x²+y²-100=0 con x-y=0
x²+y²=r²
x²+y²=100
x²+y²=10
a=x b=y c= numero
x= - c/a y= -c/b
x= -0/1 = 0
y=-0/-1 =0
Recta: Secante
2- x²+y²-36=0 con 3/2x + y-3=0
x²+y²=r²
x²+y²=36
x²+y²=6
x= -c/a y=-c/b
x= - - 3/1 / 3/2 y= - -3/1
x=6/3 y=3
Recta: secante
3- x²+y²-25=0 con 2x+y -4=0
x²+y²=r²
x²+y²=25
x²+y²=5
x=-c/a y=- c/b
x=-4/2 y=- -4/1
x=-2 y= 4
Recta: Secante
4- x²+y²-8x+6y=0 con x-y+4=0
x²-8x y²+6y
(x-4)² + (y+3)²
x²-8x+16+y²+6y+9=0
x²+y²-8x+6y+25=25
c (4,-3) r=5
x=- c/a y=- c/b
x=- 4/1 y= - 4/-1
x=-4 y=4
Recta: Ajena
5- x²+y²+6x-4y+9=0 con y=0
x²+6x y²-4y
(x+3)² + (y-2)²
x²+6x+9+y²-4y+4=0
x²+y²+6x-4y+13=4
c (-3,+2) r=2
x=- c/a y=- c/b
x=- -0/0 y= - -0/1
x=0 y=-0
Recta: ajena
6- x²+y²+4x-8y+4=0 con 3x- y-2=0
x²+4x y²-8y
(x+2)² + (y-4)²
x²+4x+4+y²-8y+16=0
x²+y²+4x-8y+20=16
c (-2,+4) r=4
x=- c/a y=- c/b
x=- -2/3 y= - -2/-1
x=.66 y=-2
Recta: tangente
7- 2x²+2y²+8x-16y+8=0 con x- y+2=0
2x²+8x 2y²-16y
(x²+4)² + (y²-8)²
x⁴+8x²+16+y⁴-16y²+64=0
x⁴+y⁴+8x²-16y²+80=72
c (-4,8) r=8.5
x=- c/a y=- c/b
x=- 2/1 y= - 2/-1
x=-2 y=2
Recta: secante
8- x²+y²-8x-8y+28=0 con x+ y-1=0
x²-8x y²-8y
(x-4)² + (y-4)²
x²-8x+16+y²-8y+16=0
x²+y²-8x-8y+32=4
c (4,4) r=2
x=- c/a y=- c/b
x=- -1/1 y= - -1/1
x=1 y=1
Recta: ajena
9- x²+y²+6x-4y+4=0 con x+ y-1=0
x²+6x y²-4y
(x+3)² + (y-2)²
x²+6x+9+y²-4y+4=0
x²+y²+6x-4y+13=9
c (-3,2) r=3
x=- c/a y=- c/b
x=- -1/1 y= - -1/1
x=1 y=1
Recta: secante
10- x²+y²+6x+6y+9=0 con x=0
x²+6x y²+6y
(x+3)² + (y+3)²
x²+6x+9+y²+6y+9=0
x²+y²+6x+6y+18=9
c (-3,-3) r=3
x=- c/a y=- c/b
x=- 0/1 y= - 0/0
x=-0 y=-0
Recta: secante
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