What is 1/4 x^2-5/4 x+1/4 y^2+9/4 y=3 ?

The solution to 1/4 x^2-5/4 x+1/4 y^2+9/4 y=3 is Circle with (a,b)=(5/2 ,-9/2),r=sqrt(77/2)

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1/4 x^2-5/4 x+1/4 y^2+9/4 y=3

\frac{1}{4} x^{2} - \frac{5}{4} x + \frac{1}{4} y^{2} + \frac{9}{4} y = 3

(a, b) = (\frac{5}{2}, - \frac{9}{2}), r = \frac{77}{2}

Solution steps

\frac{1}{4} x^{2} - \frac{5}{4} x + \frac{1}{4} y^{2} + \frac{9}{4} y = 3

Rewrite

\frac{1}{4} x^{2} - \frac{5}{4} x + \frac{1}{4} y^{2} + \frac{9}{4} y = 3

in the form of the standard circle equation

(x - \frac{5}{2})^{2} + (y - (- \frac{9}{2}))^{2} = (\frac{77}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{5}{2}, - \frac{9}{2}), r = \frac{77}{2}

(x + 4)^{2} + (y + 4)^{2} = 1 6^{2}

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

x^{2} + (y - 4)^{2} = 64

x^{2} - x + y^{2} + 3 y - \frac{6}{4} = 0

x^{2} + y^{2} - 16 x + 4 y + 43 = 0

What is 1/4 x^2-5/4 x+1/4 y^2+9/4 y=3 ?
The solution to 1/4 x^2-5/4 x+1/4 y^2+9/4 y=3 is Circle with (a,b)=(5/2 ,-9/2),r=sqrt(77/2)