SOLUTION: Find an equation of the line (in either general form or slope intercept form) that contains the centers of the following two circles: x^2+y^2-4x+6y+4 = 0 and x^2+y^2+

Question 14354: Find an equation of the line (in either general form or slope intercept form) that contains the centers of the following two circles:
x^2+y^2-4x+6y+4 = 0 and x^2+y^2+6x+4y+9 = 0
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The equation of a circle with centre as (h,k) and radius r is given by the formula
.
So we have to write the given equation in this form to get the centre of the circle.
OR
...Note that we have added and subtracted 4 and 9 to make up the squares mentioned in brackets.
Hence
Hence (2,-3)is the centre of this circle .Similarly the centre of the second circle is obtained from
OR
...Note that we have added and subtracted 9 and 4 to make up the squares mentioned in brackets.
Hence
Hence the centre of the second circle is (-3,-2)
The equation of line joining 2 ponts (x1,y1) and (x2,y2)is given by the formula

Substituting (2,-3) and (-3,-2) in the above formula we get
Y-(-3)=(-2-(-3))*(X-2)/(-3-(-2))
Y+3=(X-2)/(-5)
-5Y-15=X-2
X+5Y+13=0

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