What is x^2+y^2-1/2 x-3/2 y= 71/16 ?

The solution to x^2+y^2-1/2 x-3/2 y= 71/16 is Circle with (a,b)=(1/4 , 3/4),r= 9/4

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x^2+y^2-1/2 x-3/2 y= 71/16

x^{2} + y^{2} - \frac{1}{2} x - \frac{3}{2} y = \frac{71}{16}

(a, b) = (\frac{1}{4}, \frac{3}{4}), r = \frac{9}{4}

Solution steps

x^{2} + y^{2} - \frac{1}{2} x - \frac{3}{2} y = \frac{71}{16}

Rewrite

x^{2} + y^{2} - \frac{1}{2} x - \frac{3}{2} y = \frac{71}{16}

in the form of the standard circle equation

(x - \frac{1}{4})^{2} + (y - \frac{3}{4})^{2} = (\frac{9}{4})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{4}, \frac{3}{4}), r = \frac{9}{4}

(x^{2} - 4 x) + (y^{2} + 2 y) = 31

(x + 9)^{2} + (y + 2)^{2} = 4

x^{2} + y^{2} + 6 x - 4 y - 36 = 0

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

x^{(2)} + y^{(2)} + 2 x + 4 y - 15 = 0

What is x^2+y^2-1/2 x-3/2 y= 71/16 ?
The solution to x^2+y^2-1/2 x-3/2 y= 71/16 is Circle with (a,b)=(1/4 , 3/4),r= 9/4