Question

How do I find an equation of the line containing the centers of the following two circles? x2 +y2-4x+6y+4=0 and x2+y2+6x+4y+9=0

Answer 1

find the coordinates for the centers of each circle and find the slope between them and plug them into the line equation :)

Answer 2

(x^2-4x+n) + (y^2 +6y +m) = -4 +n +m

(x^2 -4x +4) + (y^2 +6x +9) = -4 +4 +9

(x-2)^2 + (y+3)^2 = sqrt(9) = 3

center is at (x=2, y=-3) (2,-3)

Answer 3

(x^2 +6x +n)+(y^2 +4y +m) = -9+n+m

(x^2 +6x +9) + (y^2 +4x +4) = -9 +9 +4

(x+3)^2 + (y+2)^2 = sqrt(4) = 2

center of circle is at (x=-3, y=-2) (-3,-2)

Answer 4

(2,-3) (-3,-2)

m = (y1 -y2)/(x1-x2)

m= -3--2/2--3 = -3+2/2+3 = -1/5

y = mx+b

y = (-1/5)x + b

-2=(-1/5)(-3) + b

-2 = 3/5 + b

-2 - 3/5 = b

-13/5 = b

y = (-1/5)x - 13/5 OR

x + 5y = 13

Answer 5

might want another look at that....

Answer 6

x + 5y = -13 is better :)