SOLUTION: Greetings Tutors! Please help. I've been going around and around on this problem: Find an equation of the line containing the centers of the two circles x^2 + y^2

SOLUTION: Greetings Tutors! Please help. I've been going around and around on this problem: Find an equation of the line containing the centers of the two circles x^2 + y^2 - 4x +

Question 81320This question is from textbook College Algebra
: Greetings Tutors! Please help.
I've been going around and around on this problem:
Find an equation of the line containing the centers of the two circles
x^2 + y^2 - 4x + 6y + 4 = 0
and
x^2 + y^2 + 6x + 4y + 9 = 0
I'm not even sure where to begin. Thanks in advance. This question is from textbook College Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find an equation of the line containing the centers of the two circles
x^2 + y^2 - 4x + 6y + 4 = 0
complete the square to find the center:
x^2-4x+4 +y^2+6y+9 = 9
(x-2)^2 + (y+3)^2 = 3^2
Center at (2,-3)
--------------------
and
x^2 + y^2 + 6x + 4y + 9 = 0
Complete the square to find the center:
x^2+6x+9 + y^2+4y+4 = 4
(x+3)^2 + (y+2)^2 = 262
Center at (-3,-2)
------------------
Find the equation of the line thru (2,-3) and (-3,-2)
slope = [-2--3]/[-3-2]= 1/-5 = -1/5
Form is y=mx+b where y=-3 when x=2 and where m=-1/5
-3=(-1/5)*2 + b
b= -3+2/5
b=-13/5
-----------
EQUATION you want: y=(-1/5)x-(13/5)
=======================
Cheers,
Stan H.

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