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avatar+796 

I have this question on circles

 

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

 Sep 8, 2023
 #1
avatar+126607 
+1

Rearrange as

 

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

 

To have a radius  of 1

 

50 - c   = 1

 

50  - 1 =  c

 

49  = c

 

cool cool cool

 Sep 8, 2023

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