What is ((u+v)^2)/2+((u-v)^2)/2 =1 ?

The solution to ((u+v)^2)/2+((u-v)^2)/2 =1 is Circle with (a,b)=(0,0),r=1

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((u+v)^2)/2+((u-v)^2)/2 =1

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

(a, b) = (0, 0), r = 1

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(u - 0)^{2} + (v - 0)^{2} = 1^{2}

Therefore the circle properties are:

(a, b) = (0, 0), r = 1

4 x^{2} + 12 x + 9 + 4 y^{2} > 7

x^{2} + y^{2} - 2 x - 8 y + 1 = 0

(x - 5)^{2} + (Y (x) + 2)^{2} = 16

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

2 x^{2} + 12 x + 2 y^{2} - 2 y - 3 = 0

What is ((u+v)^2)/2+((u-v)^2)/2 =1 ?
The solution to ((u+v)^2)/2+((u-v)^2)/2 =1 is Circle with (a,b)=(0,0),r=1