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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?

 Aug 10, 2024
 #1
avatar+37159 
+1

Arrange into standard circle equation form by completing the squares for x and y 

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

(x-5)^2                   + ( y+5)^2     = 50 - c            50 - c = radius ^2 

                                                                             50 - c = 1^2

                                                                                -c = -49      So    C = 49  

 Aug 10, 2024

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