Question

Obtenha o raio e o centro das circunferências a seguir:

a) x^2 +y^2 -6x -2y -6 = 0

b) x^2 +y^2 -4x -8x +16 = 0

c) x^2 +y^2 +12x -4y -9 = 0

d) x^2 +y^2 +8x + 11 = 0

Answer 1

a) -2xc=-6
xc=-6/-2=+3

-2xy=-2
xy=-2/-2=+1

r=√xc²+yc²-F
r=√3²+1²-6
r=√9+1-6
r=√4
r=2

C(3,1)

b) x²+y²-4x-8y+16=0

-2xc=-12
xc=-12/-2= +6
xy=-8/-2= +4
r=√6²+4²+16
r=√36+16-16
r=√36
r=6

C=(6,4)

c)x²+y²+12x-4y-9=0
-2xc=12
xc=12/-2= -6
-2xy=-4
xy=-4/-2=+2

r=√(-6)²+2²-(-9)
r=√36+4+9
r=√49
r=7

C=(-6,2)

d)x²+y²+8x+11=0
-2xc=8
xc=8/-2= -4
-2xy=0
xy=0/-2=0

r=√(-4)²+0²-11
r=√16-11
r=√5

C=(-4,0)