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For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?

 Mar 7, 2024
 #1
avatar+128794 
+1

x^2 -10x + y^2 + 10y  =  -c

 

Complete the square on x,y

 

x^2 -10x + 25  + y^2 + 10y + 25 =  -c + 25 + 25

 

(x + 5)^2  + ( y -5)^2   =  50  - c

 

We want

 

50 - c   =  1^2

 

50 - c  =  1

 

c  = 50 - 1 =   49

 

cool cool cool

 Mar 7, 2024

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