Prove that k1 and k2 are 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

Correct answer:

p : p=x+5y+11=0

Step-by-step explanation:

k1: x2+y2+2x+4y+1=0 k2: x2+y28x+6y+9=0  (xx0)2+(yy0)=r2  k1: (x+1)2+(y+2)=22 k2: (x  4)2 + (y + 3)2 = 42  S1 [1,2] r1=2 S2 [4,3] r2=4  ax+by+c = 0  a (1)+b (2)+c=0 a 4+b (3)+c=0 a=1  a+2bc=0 4a3b+c=0 a=1  Pivot:Row1Row2 4a3b+c=0 a+2bc=0 a=1  Row241 Row1Row2 4a3b+c=0 2.75b1.25c=0 a=1  Row341 Row1Row3 4a3b+c=0 2.75b1.25c=0 0.75b0.25c=1  Row32.750.75 Row2Row3 4a3b+c=0 2.75b1.25c=0 0.091c=1  c=0.090909091=11 b=2.750+1.25c=2.750+1.25 11=5 a=40+3bc=40+3 511=1  a=1 b=5 c=11  p:p=x+5y+11=0

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