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

The solution to 100x^2+100y^2-100x+400y+409=0 is Circle with (a,b)=(1/2 ,-2),r= 2/5

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

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

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

y^{2} = 28 x

9 x^{2} + 4 y^{2} = 1

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

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

37.2 y = x^{2}

What is 100x^2+100y^2-100x+400y+409=0 ?
The solution to 100x^2+100y^2-100x+400y+409=0 is Circle with (a,b)=(1/2 ,-2),r= 2/5