SOLUTION: Find an equation of the line containing the center of the two circles x^2-y^2-10x-6y+33=0 and x^2+y^2-4x-10y+25=0

Question 1058764: Find an equation of the line containing the center of the two circles
x^2-y^2-10x-6y+33=0 and
x^2+y^2-4x-10y+25=0
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find an equation of the line containing the center of the two circles
x^2-y^2-10x-6y+33=0 and
x^2+y^2-4x-10y+25=0
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Step 1, find the centers.
I'll do 1:
x^2-y^2-10x-6y+33=0
That's not a circle, it's a hyperbola.
If you meant x^2+y^2-10x-6y+33=0
Complete the squares of x and y separately.
x^2+y^2-10x-6y+33=0
x^2 - 10x + y^2 - 6y = -33
x^2 - 10x + 25 + y^2 - 6y + 9 = -33 + 25 + 9 = 1
(x-5)^2 + (y-3)^2 = 1
Center at (5,3)
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Find the other center.
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Then find the slope, m, of the line between the 2 points.
Then use y-y1 = m*(x-x1) where (x1,y1) is either point.

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