What is ((2x-2)^2)/2+((2y+6)^2)/2 = 46/2 ?

The solution to ((2x-2)^2)/2+((2y+6)^2)/2 = 46/2 is Circle with (a,b)=(1,-3),r=sqrt(23/2)

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((2x-2)^2)/2+((2y+6)^2)/2 = 46/2

\frac{( 2 x - 2 ) ^{2}}{2} + \frac{( 2 y + 6 ) ^{2}}{2} = \frac{46}{2}

(a, b) = (1, - 3), r = \frac{23}{2}

Solution steps

\frac{( 2 x - 2 ) ^{2}}{2} + \frac{( 2 y + 6 ) ^{2}}{2} = \frac{46}{2}

Rewrite

\frac{( 2 x - 2 ) ^{2}}{2} + \frac{( 2 y + 6 ) ^{2}}{2} = \frac{46}{2}

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 3))^{2} = (\frac{23}{2})^{2}

Therefore the circle properties are:

(a, b) = (1, - 3), r = \frac{23}{2}

x^{2} + y^{2} - 8 x + 10 y + 32 = 0

x^{2} + (y - \frac{16}{3})^{2} = 49

x^{2} + y^{2} - 2 x - 2 y + 4 + 5 - 64 = 0

x^{2} + 2 x + y^{2} - 5 = 0

\frac{( u + v ) ^{2}}{2} + \frac{( u - v ) ^{2}}{2} = 1

What is ((2x-2)^2)/2+((2y+6)^2)/2 = 46/2 ?
The solution to ((2x-2)^2)/2+((2y+6)^2)/2 = 46/2 is Circle with (a,b)=(1,-3),r=sqrt(23/2)