What is x^2+(y^2-3y-9/4)=3+9/4 ?

The solution to x^2+(y^2-3y-9/4)=3+9/4 is Circle with (a,b)=(0, 3/2),r=(sqrt(39))/2

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x^2+(y^2-3y-9/4)=3+9/4

x^{2} + (y^{2} - 3 y - \frac{9}{4}) = 3 + \frac{9}{4}

(a, b) = (0, \frac{3}{2}), r = \frac{39}{2}

Solution steps

x^{2} + (y^{2} - 3 y - \frac{9}{4}) = 3 + \frac{9}{4}

Rewrite

x^{2} + (y^{2} - 3 y - \frac{9}{4}) = 3 + \frac{9}{4}

in the form of the standard circle equation

(x - 0)^{2} + (y - \frac{3}{2})^{2} = (\frac{39}{2})^{2}

Therefore the circle properties are:

(a, b) = (0, \frac{3}{2}), r = \frac{39}{2}

x^{2} + y^{2} - 1 0^{2} = 0

\frac{1}{25} (x^{2} + y^{2}) = 1

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

x^{2} + 2 x + y^{2} - \frac{2}{3} y + \frac{1}{2} = 0

x^{2} + y^{2} + 2 x + 8 y + 13 = 0

What is x^2+(y^2-3y-9/4)=3+9/4 ?
The solution to x^2+(y^2-3y-9/4)=3+9/4 is Circle with (a,b)=(0, 3/2),r=(sqrt(39))/2