What is (2x-1)^2+(2y-1)^2=1 ?

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

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(2x-1)^2+(2y-1)^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{2} - 14 x + y^{2} + 12 y = 36

x^{2} + y^{2} - 8 x - 12 y + 48 = 0

9 - x^{2} - y^{2} > 0

x^{2} + x + y^{2} + 11 y - 32 = 0

x^{2} + y^{2} + 6 x - 8 y = - 9

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