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 + 1)^{2} + (Y - 4)^{2} = 25

2 = 16 - x^{2} - y^{2}

(x - 10)^{2} + (y - 6)^{2} = 1

x^{2} + y^{2} - 18 x + 16 y + 81 = 0

(x + 2)^{2} + y^{2} = 8 y - 7

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