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avatar+1791 

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle.  Find the radius of the circle.

 Apr 24, 2024
 #1
avatar+128794 
+1

Rearrange as

 

4x^2 - 8x + 4y^2 + 14y  = -12     divide through by 4

 

x^2  - 2x + y^2 + (7/2)y =  -3      complete the square on x, y

 

x^2 - 2x + 1  +  y^2 + (7/2)y + 49 /16 =  -3 + 1 + 49/16

 

(x - 1)^2  + (y + 7/4)^2  = 17 / 16

 

The radius =   sqrt ( 17/16)  =   sqrt (17) / 4

 

 

cool cool cool

 Apr 24, 2024

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