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The equation of the circle shown in the following diagram can be written as \(x^2 + Ay^2 + Bx + Cy + D = 0\) . Find \(A+B+C+D\).

 

https://latex.artofproblemsolving.com/d/4/b/d4b6468bc485090058e6cdadf256aca42c141d53.png

 Feb 5, 2018
 #1
avatar+100516 
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The center is  ( -1, 1)

 

And the radius  is   √5

 

So....the equation is

 

(x + 1)^2  + (y - 1)^2  = 5        simplify

 

x^2 + 2x + 1  + y^2 - 2y + 1  =  5

 

x^2 + 1y^2 + 2x - 2y - 3  =  0

 

So

 

A + B + C + D  =

 

1 + 2 -  2   - 3  =     -2 

 

 

cool cool cool

 Feb 5, 2018

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