Prove

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

Final Answer:

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

Step-by-step explanation:

k1​: x2+y2+2x+4y+1=0 k2​: x2+y2−8x+6y+9=0  (x−x0​)2+(y−y0​)=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+2b−c=0 4a−3b+c=0 a=1  Pivot:Row1↔Row2  Row2−41​⋅ Row1→Row2 2.75b−1.25c=0  Row3−41​⋅ Row1→Row3 0.75b−0.25c=1  Row3−2.750.75​⋅ Row2→Row3 0.091c=1  c=0.090909091​=11 b=2.750+1.25c​=2.750+1.25⋅ 11​=5 a=40+3b−c​=40+3⋅ 5−11​=1  b=5 c=11  p:p=x+5y+11=0

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geometryalgebraplanimetricsbasic operations and conceptsthemes, topicsGrade of the word problem

 
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