SOLUTION: Given the equation of the circle is {{{x^2-4x+y^2-6y=3}}}. Find the equation of the circle in the form{{{(x-a)^2+(y-b)^2=r^2}}}. Hence find out the centre, area and circumference o

Algebra ->  Circles -> SOLUTION: Given the equation of the circle is {{{x^2-4x+y^2-6y=3}}}. Find the equation of the circle in the form{{{(x-a)^2+(y-b)^2=r^2}}}. Hence find out the centre, area and circumference o      Log On


   

Question 975231: Given the equation of the circle is x%5E2-4x%2By%5E2-6y=3. Find the equation of the circle in the form%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2. Hence find out the centre, area and circumference of the circle.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given the equation of the circle is x%5E2-4x%2By%5E2-6y=3.
x^2-4x + 4 + y^2-6y+9 = 3 +4+9
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(x-2)^ + (y-3)^2 = 16
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Find the equation of the circle in the form%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2.
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Hence find out the
centre:: (2,3)
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area = pi*4^2 = 16pi square units
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circumference of the circle = 2*pi*4 = 8pi units
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-4x%2By%5E2-6y=3 in form %28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2
%28x%5E2-4x%29%2B%28y%5E2-6y%29=3......complete squares
%28x%5E2-4x%2Bb%5E2%29-b%5E2%2B%28y%5E2-6y%2Bb%5E2%29-b%5E2=3
%28x%5E2-4x%2B2%5E2%29-2%5E2%2B%28y%5E2-6y%2B3%5E2%29-3%5E2=3
%28x-2%29%5E2-4%2B%28y-3%29%5E2-9=3
%28x-2%29%5E2%2B%28y-3%29%5E2-13=3
%28x-2%29%5E2%2B%28y-3%29%5E2=3%2B13
%28x-2%29%5E2%2B%28y-3%29%5E2=16
%28x-2%29%5E2%2B%28y-3%29%5E2=4%5E2
so, h=2, k=3, and r=4
the center is at (2,3)