What is 8x+x^{(2)}-2y=64-y^{(2)} ?

The solution to 8x+x^{(2)}-2y=64-y^{(2)} is Circle with (a,b)=(-4,1),r=9

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8x+x^{(2)}-2y=64-y^{(2)}

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

(a, b) = (- 4, 1), r = 9

Solution steps

8 x + x^{2} - 2 y = 64 - y^{2}

Rewrite

8 x + x^{2} - 2 y = 64 - y^{2}

in the form of the standard circle equation

(x - (- 4))^{2} + (y - 1)^{2} = 9^{2}

Therefore the circle properties are:

(a, b) = (- 4, 1), r = 9

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

4 x^{2} + 36 x + 4 y^{2} - 8 y + 68 = x^{2} - 6 x + y^{2} - 4 y + 13

x^{2} + (y - 1)^{2} = 16

(x^{2} - 10 x + 25) + (y^{2} + 4 y + 4) = 36

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

What is 8x+x^{(2)}-2y=64-y^{(2)} ?
The solution to 8x+x^{(2)}-2y=64-y^{(2)} is Circle with (a,b)=(-4,1),r=9