What is the radius x^2+y^2+8y=2x+20 ?

The radius x^2+y^2+8y=2x+20 is r=sqrt(37)

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radius x^2+y^2+8y=2x+20

radius

x^{2} + y^{2} + 8 y = 2 x + 20

r = 37

Solution steps

x^{2} + y^{2} + 8 y = 2 x + 20

Rewrite

x^{2} + y^{2} + 8 y = 2 x + 20

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 4))^{2} = (37)^{2}

Therefore the circle properties are:

(a, b) = (1, - 4), r = 37

And the radius is:

r = 37

(x - 2)^{2} + (y - 5)^{2} = 49

x^{2} - 6 x + y^{2} = 7

(x^{2} - 2) + (y^{2} + 4) = 16

4 x^{2} + 4 x + 4 y^{2} - 16 y - 19 = 0

2 x^{2} + 2 y^{2} + 8 x - 12 y - 26 = 0