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

 Jun 18, 2024
 #1
avatar+129733 
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Simplify 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

 

r^2  = -2 + 49/16  =  [- 32 + 49 ] / 16  =  17 /16

 

r  = sqrt (17) /  4

 

cool cool cool

 Jun 18, 2024

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