What is 4y^2=-4x^2+12y-69+32x ?

The solution to 4y^2=-4x^2+12y-69+32x is Circle with (a,b)=(4, 3/2),r=1

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4y^2=-4x^2+12y-69+32x

4 y^{2} = - 4 x^{2} + 12 y - 69 + 32 x

(a, b) = (4, \frac{3}{2}), r = 1

Solution steps

4 y^{2} = - 4 x^{2} + 12 y - 69 + 32 x

Rewrite

4 y^{2} = - 4 x^{2} + 12 y - 69 + 32 x

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (4, \frac{3}{2}), r = 1

9 x^{2} + 9 y^{2} + 72 x - 12 y + 103 = 0

9 x^{2} + 9 y^{2} - 12 x + 36 y - 104 = 0

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

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

(x + 3)^{2} + (y - 2)^{2} = 1

What is 4y^2=-4x^2+12y-69+32x ?
The solution to 4y^2=-4x^2+12y-69+32x is Circle with (a,b)=(4, 3/2),r=1