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For what value of c will the circle with equation x^2 + 8x + y^2 + 6y + c = 0 have a radius of length \(3\)?

 Jan 30, 2022
 #1
avatar+1209 
+2

x^2 + 8x + y^2 + 6y = -c

(x + 4)^2 + (y + 3)^2 = -c + 16 + 9 = -c + 25

 

The equation of a circle is (x - h)^2 + (y - k)^2 = r^2. So, we want:

 

-c + 25 = 3^2 = 9

 

c = 16.

 Jan 30, 2022
 #2
avatar+36417 
+2

x^2 + 8x + y^2 + 6 y   = - c     complete the square for x and y

(x+4)^2     +  (y+3)^2   =  16 + 9 - c       red part = radius ^2

                                         25 - c = 3^2

                                             - c = -16

                                                c = 16

 Jan 30, 2022
edited by ElectricPavlov  Jan 30, 2022

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