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Let \(C\)  be the circle with equation \(x^2-6y-3=-y^2-4x\) . If (a,b) is the center of \(C\)  and \(r\)  is its radius, what is the value of a+b+r?

ant101  Mar 14, 2017
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x^2 - 6y - 3 = -y^2 - 4x    rearrange as

 

x^2 + 4x + y^2 - 6y = 3      complete the square on x and y

 

x^2 + 4x + 4  +  y^2 -6y + 9  =  3 + 4 + 9     factor and simplify

 

(x + 2)^2  + (y - 3)^2  = 16

 

The center is  (-2, 3)   and the radius = 4

 

So  a + b + r   =   -2 + 3 + 4  =   5

 

 

cool cool cool

CPhill  Mar 14, 2017

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