What is the radius (x-5)^2+(y+1)^2=16 ?

The radius (x-5)^2+(y+1)^2=16 is r=4

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radius (x-5)^2+(y+1)^2=16

radius

(x - 5)^{2} + (y + 1)^{2} = 16

r = 4

Solution steps

(x - 5)^{2} + (y + 1)^{2} = 16

Rewrite

(x - 5)^{2} + (y + 1)^{2} = 16

in the form of the standard circle equation

(x - 5)^{2} + (y - (- 1))^{2} = 4^{2}

Therefore the circle properties are:

(a, b) = (5, - 1), r = 4

And the radius is:

r = 4

(x - 3)^{2} + (y + 4)^{2} = 16

x^{2} + y^{2} + 4 x + 20 y + 23 = 0

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

x^{2} - 8 x + y^{2} - 10 y = 40

6 x^{2} + 6 y^{2} - 24 x + 36 y = 72