# Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles.

k1: x2+y2+2x+4y+1=0
k2: x2+y2-8x+6y+9=0

Result

p = (Correct answer is: p=x+5y+11=0)

#### Solution:

$k_{1}: x^2+y^2+2x+4y+1=0 \ \\ k_{2}: x^2+y^2-8x+6y+9=0 \ \\ \ \\ (x-x_{0})^2+(y-y_{0})=r^2 \ \\ \ \\ k_{1}: (x+1)^2+(y+2)=2^2 \ \\ k_{2}: (x - 4)^2 + (y + 3)^2=4^2 \ \\ \ \\ S_{1} [-1,-2] \ \\ r_{1}=2 \ \\ S_{2} [4,-3] \ \\ r_{2}=4 \ \\ \ \\ ax+by+c=0 \ \\ \ \\ a \cdot \ (-1)+b \cdot \ (-2)+c=0 \ \\ a \cdot \ 4+b \cdot \ (-3)+c=0 \ \\ a=1 \ \\ \ \\ a+2b-c=0 \ \\ 4a-3b+c=0 \ \\ a=1 \ \\ \ \\ a=1 \ \\ b=5 \ \\ c=11 \ \\ \ \\ p=x+5y+11=0$

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