What is 4x^2+4y^2-4x+2y=1 ?

The solution to 4x^2+4y^2-4x+2y=1 is Circle with (a,b)=(1/2 ,-1/4),r= 3/4

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4x^2+4y^2-4x+2y=1

4 x^{2} + 4 y^{2} - 4 x + 2 y = 1

(a, b) = (\frac{1}{2}, - \frac{1}{4}), r = \frac{3}{4}

Solution steps

4 x^{2} + 4 y^{2} - 4 x + 2 y = 1

Rewrite

4 x^{2} + 4 y^{2} - 4 x + 2 y = 1

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - (- \frac{1}{4}))^{2} = (\frac{3}{4})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - \frac{1}{4}), r = \frac{3}{4}

x^{2} + y^{2} + 3 x + y - 10 = 0

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

x^{2} + y^{2} - 10 x - 24 y + 25 = 0

x^{2} - 2 x + 1 + y^{2} - 4 y + 4 = 196

(x - 3)^{2} + (Y (x) - (- 2))^{2} = (\frac{1}{2})^{2}

What is 4x^2+4y^2-4x+2y=1 ?
The solution to 4x^2+4y^2-4x+2y=1 is Circle with (a,b)=(1/2 ,-1/4),r= 3/4