What is 4x^2+4y^2-6x+10y= 1/2 ?

The solution to 4x^2+4y^2-6x+10y= 1/2 is Circle with (a,b)=(3/4 ,-5/4),r= 3/2

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4x^2+4y^2-6x+10y= 1/2

4 x^{2} + 4 y^{2} - 6 x + 10 y = \frac{1}{2}

(a, b) = (\frac{3}{4}, - \frac{5}{4}), r = \frac{3}{2}

Solution steps

4 x^{2} + 4 y^{2} - 6 x + 10 y = \frac{1}{2}

Rewrite

4 x^{2} + 4 y^{2} - 6 x + 10 y = \frac{1}{2}

in the form of the standard circle equation

(x - \frac{3}{4})^{2} + (y - (- \frac{5}{4}))^{2} = (\frac{3}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{3}{4}, - \frac{5}{4}), r = \frac{3}{2}

(x + 15)^{2} + (y - 12)^{2} = 64

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

(x - 2)^{2} + (y + 4)^{2} = 36

4 x^{2} + 4 y^{2} - 40 x - 8 y + 40 = 0

(x - 0)^{2} + (y - 5)^{2} = (4)^{2}

What is 4x^2+4y^2-6x+10y= 1/2 ?
The solution to 4x^2+4y^2-6x+10y= 1/2 is Circle with (a,b)=(3/4 ,-5/4),r= 3/2