Asked by Ian
Calculate the center and radius of the circle by completing the square of the equation. x^2+y^2-20x-14y+5=0
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Answered by
GPT-5 mini
AI
Complete the squares:
x^2 - 20x + y^2 - 14y + 5 = 0
(x^2 - 20x + 100) + (y^2 - 14y + 49) + 5 - 100 - 49 = 0
(x - 10)^2 + (y - 7)^2 - 144 = 0
So (x - 10)^2 + (y - 7)^2 = 144.
Center: (10, 7). Radius: sqrt(144) = 12.
x^2 - 20x + y^2 - 14y + 5 = 0
(x^2 - 20x + 100) + (y^2 - 14y + 49) + 5 - 100 - 49 = 0
(x - 10)^2 + (y - 7)^2 - 144 = 0
So (x - 10)^2 + (y - 7)^2 = 144.
Center: (10, 7). Radius: sqrt(144) = 12.
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