What is the radius 100x^2+100y^2-100x+400y+409=0 ?

The radius 100x^2+100y^2-100x+400y+409=0 is r= 2/5

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radius 100x^2+100y^2-100x+400y+409=0

radius

100 x^{2} + 100 y^{2} - 100 x + 400 y + 409 = 0

r = \frac{2}{5}

Solution steps

100 x^{2} + 100 y^{2} - 100 x + 400 y + 409 = 0

Rewrite

100 x^{2} + 100 y^{2} - 100 x + 400 y + 409 = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - 2), r = \frac{2}{5}

And the radius is:

r = \frac{2}{5}

x^{2} + y^{2} + 6 x - 4 y - 23 = 0

x^{2} + y^{2} - 4 x + 8 y - 5 = 0

x^{2} + y^{2} + 8 x - 9 y = 6

x^{2} + y^{2} + 12 x - 12 y + 36 = 0

x^{2} + y^{2} + 6 x - 4 y - 12 = 0

What is the radius 100x^2+100y^2-100x+400y+409=0 ?
The radius 100x^2+100y^2-100x+400y+409=0 is r= 2/5