What is y=x^{(2)}-4x+y^{(2)} ?

The solution to y=x^{(2)}-4x+y^{(2)} is Circle with (a,b)=(2, 1/2),r=(sqrt(17))/2

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y=x^{(2)}-4x+y^{(2)}

y = x^{(2)} - 4 x + y^{(2)}

(a, b) = (2, \frac{1}{2}), r = \frac{17}{2}

Solution steps

y = x^{2} - 4 x + y^{2}

Rewrite

y = x^{2} - 4 x + y^{2}

in the form of the standard circle equation

(x - 2)^{2} + (y - \frac{1}{2})^{2} = (\frac{17}{2})^{2}

Therefore the circle properties are:

(a, b) = (2, \frac{1}{2}), r = \frac{17}{2}

x^{2} - 6 x + y^{2} = 16

4 x^{2} + 8 x + 4 y^{2} + 4 = 16

x^{2} - \frac{5}{2} x + (y + 2)^{2} = 50

4 = x^{2} + y^{2} - 2 x + 4 y

(x - 12)^{2} + (y + 7)^{2} = 961

What is y=x^{(2)}-4x+y^{(2)} ?
The solution to y=x^{(2)}-4x+y^{(2)} is Circle with (a,b)=(2, 1/2),r=(sqrt(17))/2