PARABOLAS, CIRCUNSFERENCIAS, Ejercicios de Matemáticas

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9 = b - 1

25 = 16+ (b-1)

25 = (-4) + (b-1)

25 - 16 = (b-1)

3 = b - 1

4 = b

5 = (3-7) + (b-1)

Gráfica

P = (x,y) dAP = (x-2) + (y-3) dBP = (x-4) + (y+1) dCP^ =^ (x-5) + (y-2) (x-2) + (y-3) (x-4) + (y+1) (x-2) + (y-3) (x-4) + (y+1) x -4x+4+y -6y+9 = x -8x +16 +y +2y+ 4x - 8y - 4 = 0 ec. 01 (x-4) + (y+1) (x-5) + (y-2) (x-4) + (y+1) (x-5) + (y-2) x -8x+16+y+2y+1 = x -10x+25+y -4y+ 2x + 6y - 12 = 0 ec. 02 4x - 8y - 4 = 0 2x + 6y - 12 = 0 (-2) -4x - 12y + 24 = 0 4x - 8y - 4 = 0

• 20y +20 = 0 -20y = - y = 1 4x - 8(1) - 4 = 0 4x - 8 - 4 = 0 4x - 12 = 0 x = 3

P = (3,1)

dAP = dBP dBP =^ dCP

dAP = (x+11) + (y-3) (^) dBP = (x-6) + (y-10) dCP = (x-1) + (y-11) P = (x,y) (x+11)+(y-3) (x-6) + (y-10) x +22x+121+y -6y+9 = x -12x +36 +y-20y+ 34x + 14y - 6 = 0 ec. 01 (x-6) + (y-10) (x-1) + (y-11) -10x + 2y + 14 = 0 ec. 02

dAP = dBP dBP =^ dCP

(x+11)+ (y-3) (x-6) + (y-10) x -12x +36 +y-20y+100 = x -2x+1+y -22y+ (x-6) + (y-10) (x-1) + (y-11) 70x - 14y - 98 = 0 34x + 14y - 6 = 0 104x - 104 = 0 104x = 104 x = 1 34x + 14y - 6 = 0 -10x + 2y + 14 = 0 (-7) -10(1) + 2y+ 14 = 0 -10+ 2y + 14 = 0 2y + 4 = 0 2y = - y = -

P = (1,-2)

P = (x,0) N = (2,-3) d = 5 (x-2) + (0+3) = 5 (x-2) + 9 = 25 (x-2) = 16 x-2 = 16 x-2 = 4 x = 4 + 2 P 1 = (-2,0) P 2 = (6,0) (x-2) + (0+3) = 5 x = 6 x = -

P Q (x ;y ) A B (x;y) (2;2) (1;5) A = (3;-1) B = (0;8)

2(x - 3) = 5 (-2 + 4) 2x - 6 = -10 + 20 2x = 16 x = 8 2(-10) = 5 (y + 4) -20 = 5y + 20 -40 = 5y y = -

M= (4,5) (1,2)

y - 4 = 0

y = 4

y - 2 = 0

y = 2

y = x -

25 = (x-3) + (y-2)

25 = x - 6x + 9 + y - 4y + 4

25 = x - 6x + 9 + y - 4y + 4

25 = x + y - 6x - 4y + 13

25 = x + ( ) - 6x - 4 ( ) + 13

25 = x +

y = x -

y = x -

P = (7,5)

Q = (-1,-1)

5 = (x-3) + (y-2)

y - 2 = (x - 3)

D (4,7) M (-1,3) N (4,0) Punto de intersección: (4, )

Ecuación de la circunferenca

AC = BC (1-x) + (4-y) 9+6x+x +9-6y+y = 1-2x+x +16-8y+y 8x + 2y + 1 = 0 8(2) + 2y + 1 = 0 16 + 2y + 1 = 0 17 + 2y = 0 2y = - C = (2, ) (-3-2) + (3-( )) = r r = 12. Ecuacion de la circunferencia Forma general (-3-x) + (3-y) 3x -2y - 23 = 0 8x + 2y + 1 = 0 11x - 22 = 0 11x = 22 x = 2

Al ser tangente al eje "x" en A= (4,0), se tiene que: donde 4 = h Ecuación de la circunferencia

ec. 1

A

ec. 2

B

ec. 3

C

ec.

ec.

4(-2)-3(-2)+E = -

-8+6+E = -

-2+E = -

E = -

x + y - 2x - 2y - 23 = 0 Ecuación en forma general

x - 2x +1+ y - 2y + 1= 23+1+

(x - 1) + (y - 1) = 25 Ecuación en forma ordinaria

h = 1

k = 1

r = 25

r = 5

C = (1,1) r = 5

V = (0,0) F = (3,0) Ecuación