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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?

 Jan 30, 2025
 #1
avatar+130383 
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Complete the square on x, y

 

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

 

(x -5)^2  + ( y+ 5)^2  =  50   - c

 

We want 50 - c  =1

 

c =  49

 

 

cool cool cool

 Jan 30, 2025

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