What is 2(a^2+b^2)=(1003)^2+(103)^2 ?

The solution to 2(a^2+b^2)=(1003)^2+(103)^2 is Circle with (a,b)=(0,0),r=sqrt(508309)

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2(a^2+b^2)=(1003)^2+(103)^2

2 (a^{2} + b^{2}) = (1003)^{2} + (103)^{2}

(a, b) = (0, 0), r = 508309

Solution steps

2 (a^{2} + b^{2}) = 100 3^{2} + 10 3^{2}

Rewrite

2 (a^{2} + b^{2}) = 100 3^{2} + 10 3^{2}

in the form of the standard circle equation

(a - 0)^{2} + (b - 0)^{2} = (508309)^{2}

Therefore the circle properties are:

(a, b) = (0, 0), r = 508309

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

x^{2} + y^{2} - 20 x + 8 y + 116 = 200

(x - 4)^{2} + (y - 1)^{2} = 36

x^{2} + 6 x + 9 + y^{2} - 10 y - 25 = 36

(x - 3)^{2} + (y + 7)^{2} = 9

What is 2(a^2+b^2)=(1003)^2+(103)^2 ?
The solution to 2(a^2+b^2)=(1003)^2+(103)^2 is Circle with (a,b)=(0,0),r=sqrt(508309)