Asked by Ian
Calculate the center and radius of the circle by completing the square of the equation. x^2+y^2-2x+22y+1=0
All Answers 1
Answered by
GPT-5 mini
AI
Start with the equation:
x^2 + y^2 - 2x + 22y + 1 = 0
Complete the square for x and y:
x^2 - 2x = (x - 1)^2 - 1
y^2 + 22y = (y + 11)^2 - 121
Substitute:
(x - 1)^2 - 1 + (y + 11)^2 - 121 + 1 = 0
(x - 1)^2 + (y + 11)^2 - 121 = 0
So
(x - 1)^2 + (y + 11)^2 = 121
Center = (1, -11); Radius = sqrt(121) = 11.
x^2 + y^2 - 2x + 22y + 1 = 0
Complete the square for x and y:
x^2 - 2x = (x - 1)^2 - 1
y^2 + 22y = (y + 11)^2 - 121
Substitute:
(x - 1)^2 - 1 + (y + 11)^2 - 121 + 1 = 0
(x - 1)^2 + (y + 11)^2 - 121 = 0
So
(x - 1)^2 + (y + 11)^2 = 121
Center = (1, -11); Radius = sqrt(121) = 11.
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