SOLUTION: Find an equation of the line containing the centers of the two circles x^2+y^2-10x-10y+49 and x^2+y^2-4x-6y+9=0

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find an equation of the line containing the centers of the two circles x^2+y^2-10x-10y+49 and x^2+y^2-4x-6y+9=0      Log On


   

Question 932193: Find an equation of the line containing the centers of the two circles
x^2+y^2-10x-10y+49 and x^2+y^2-4x-6y+9=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the centers.
x%5E2-10x%2By%5E2-10y%2B49=0
%28x%5E2-10x%2B25%29%2B%28y%5E2-10y%2B25%29%2B49=25%2B25
%28x-5%29%5E2%2B%28y-5%29%5E2=1
(5,5) with a radius of 1.
.
.
x%5E2-4x%2By%5E2-6y%2B9=0
%28x%5E2-4x%2B4%29%2B%28y%5E2-6y%2B9%29%2B9=4%2B9
%28x-2%29%5E2%2B%28y-3%29%5E2=4
(2,3) with a radius of 2.
Find the slope,
m=%285-3%29%2F%285-2%29=2%2F3
Use the point-slope form,
y-5=%282%2F3%29%28x-5%29
y-5=%282%2F3%29x-10%2F3
y=%282%2F3%29x-10%2F3%2B15%2F3
highlight%28y=%282%2F3%29x%2B5%2F3%29
.
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