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

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

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

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

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

Solution steps

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

Rewrite

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

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 - 7)^{2} + (y - 3)^{2} = 4

5 x^{2} + 5 y^{2} + 100 x + 50 y + 220 = 0

x^{2} + y^{2} \leq 4 x

3 x^{2} + 3 y^{2} - 24 x - 24 y - 51 = 0

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

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