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anonymous
 one year ago
Find the area between two concentric circles defined by
x2 + y2 2x + 4y + 1 = 0
x2 + y2 2x + 4y  11 = 0
anonymous
 one year ago
Find the area between two concentric circles defined by x2 + y2 2x + 4y + 1 = 0 x2 + y2 2x + 4y  11 = 0

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3You can complete the squares in both equations and find the radii of the circles. Then find the areas of the circles and find the difference.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Do you know how to complete the square?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3The equation of a circle with center \((h, k)\) and radius \(r\) is \((x  h)^2 + (y  k)^2 = r^2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3For each equation you are given, you need to complete the square of the x variable and complete the square of the y variable. Then you'll be able to tell what the center is (which we really don't need to know) and what the radius is (which is what we want).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So is the equation (x  1)2 + (y + 2) 2 = 4 = 22 and for the second one is it (x  1)2 + (y + 2) 2 = 16 = 42

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I meant \[2^{2}\] and \[4^{2}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\color{red}{x^2} + \color{green}{y^2} + \color{red}{( 2x)} + \color{green}{4y} + 1 = 0 \) \(\color{red}{x^2 2x} + \color{green}{y^2 +4y} + = 1 \) \(\color{red}{x^2 2x + 1} + \color{green}{y^2 +4y + 4} + = 1 + \color{red}{1} + \color{green}{4}\) \(\color{red}{(x  1)^2} + \color{green}{(y + 2)^2} = 2^2\) The first radius is 2.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(x^2 + y^2 2x + 4y  11 = 0 \) \(x^2 2x + y^2 + 4y = 11 \) \(x^2 2x + 1 + y^2 + 4y + 4 = 11+1+4 \) \((x 1)^2 + (y+ 2)^2 = 4^2 \) The radius of the second one is 4. You are correct again.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Now find the area of a circle with radius 4 and find the area of a circle with radius 2. Then find the difference of the areas.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Large circle has radius R and small circle has radius r. \(\large A_{ring} = \pi R^2  \pi r^2 = \pi (R^2  r^2)\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\large A_{ring} = \pi R^2  \pi r^2 = \pi (R^2  r^2) =\color{red}{\pi (4^2  2^2) = \pi (16  4) = 12 \pi} \) You are correct. Great job!
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