Find an equation of the line containing the centers of the two circles given below.
x^2 + y^2 - 4x + 6y + 4 = 0 and
x^2 + y^2 + 6x + 4y + 9n= 0.
Seeking the first-two steps.
The first equation is (x - 2)^2 + (y + 3)^2 = 25. The center (h, k) is (2, -3).
The second equation is (x + 3)^2 + (y + 2)^2 = 16. The center (h, k) is (-3, -2).
Let x_1 = 2, y_1 = -3, x_2 = -3 and y_2 = -2.
We now plug and chug.
y = [(-2 -(-3))/(-3 -2)](x - 2) - 3
y = [(-2 + 3)/-5](x - 2) - 3
y = (-1/5)(x - 2) - 3
y = [-(x - 2)/5] - 3
Correct?
Final equation is correct. You are not getting the centre/radius from of the circle correct though.
Equations of lines are usually written in:
gradient-intercept form: y=mx + c , in this case $\displaystyle y=\frac{-1}{5}x - \frac{13}{5}$
or
standard form: ax+ by +c =0 , in this case x + 5y + 13 =0