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The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = 3x^2 + 3y^2 + 2x - 4y
is a circle.  Find the radius of the circle.

 Dec 29, 2023
 #1
avatar+129477 
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Simplify as

 

x^2 - 14x + y^2 + 20y = -17           complete the square on x, y

 

x^2 - 14x + 49  + y^2 + 20y + 100  = -17 + 49 + 100

 

( x - 7)^2  + ( y + 10)^2  = 132

 

The center is (7, -10)   and the radius =  sqrt (132)  =  = sqrt (4 * 33)  = 2sqrt (33)

 

cool cool cool

 Dec 29, 2023

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