## kcbrosell 3 years ago Find an equation of the line containing the centers of the two circles x2 + y2 − 4x + 6y + 4 = 0 and x2 + y2 + 6x + 4y + 9 = 0 I have an answer for this 1 but I want to make sure I am right.

1. GT

What are the points of the centers of the circles you have?

2. MrYantho

Do you know how to find the centres of the circles? Circle one is (2,-3) I believe

3. kcbrosell

The ? I asked is the only thing on the paper so I dont know what the points are

4. MrYantho

Oh, you said you had an answer. Would you like me to show you how to find the centres of the circles?

5. kcbrosell

Yes I would, I came up with Neither

6. MrYantho

You have to 'complete the square' for both the x terms and y terms. This is because you need the equation in standard form. \[x ^{2}+y ^{2}-4x+6y+4=0\] Gather \[x ^{2}-4x+y ^{2}+6y+4=0\] \[(x ^{2}-4x)+(y ^{2}+6y)+4=0\] Now comes the complete the square part \[(x ^{2}-4x+4-4)+(y ^{2}+6y+9-9)+4=0\] \[(x ^{2}-4x+4)-4+(y ^{2}+6y+9)-9+4=0\] simplify \[(x ^{2}-4x+4)+(y ^{2}+6y+9)-9=0\] Factor our x and y terms \[(x-2)^{2}+(y+3)^{2}=9\] this means the centre of the circle is (2,-3)