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For what value of c will the circle with equation x^2 + 6x + y^2 - 4y - 10x - 12y + c = 0 have a radius of length 4?

 Apr 24, 2022

Best Answer 

 #2
avatar+124594 
-1

Rearrange as

 

x^2  - 4x + y^2 - 16 y  =   -c     complete the square on x , y

 

(x^2  - 4x + 4)  + ( y^2  - 16y  + 64 )  =  -c + 4  + 64

 

We want    

 

-c + 4 + 64  =   r^2

 

-c + 68  =  4^2

 

-c =  16 -  68

 

c =  68   -  16

 

c =  52

 

 

cool cool cool

 Apr 24, 2022
 #1
avatar
0

c = -76.

 Apr 24, 2022
 #2
avatar+124594 
-1
Best Answer

Rearrange as

 

x^2  - 4x + y^2 - 16 y  =   -c     complete the square on x , y

 

(x^2  - 4x + 4)  + ( y^2  - 16y  + 64 )  =  -c + 4  + 64

 

We want    

 

-c + 4 + 64  =   r^2

 

-c + 68  =  4^2

 

-c =  16 -  68

 

c =  68   -  16

 

c =  52

 

 

cool cool cool

CPhill Apr 24, 2022

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