What is 100x^2+100y^2-100x+240y-56=0 ?

The solution to 100x^2+100y^2-100x+240y-56=0 is Circle with (a,b)=(1/2 ,-6/5),r= 3/2

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100x^2+100y^2-100x+240y-56=0

100 x^{2} + 100 y^{2} - 100 x + 240 y - 56 = 0

(a, b) = (\frac{1}{2}, - \frac{6}{5}), r = \frac{3}{2}

Solution steps

100 x^{2} + 100 y^{2} - 100 x + 240 y - 56 = 0

Rewrite

100 x^{2} + 100 y^{2} - 100 x + 240 y - 56 = 0

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - (- \frac{6}{5}))^{2} = (\frac{3}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - \frac{6}{5}), r = \frac{3}{2}

a^{2} - 2 \frac{1}{2} + b^{2} = 1

x^{2} + y^{2} + 3 y + \frac{7}{4} = 0

x^{2} + (y - 1)^{2} \leq 1

(x + 1)^{2} + (y + 3)^{2} = 7. 9^{2}

a^{2} - 2 a + b^{2} - 2 b \geq 0

What is 100x^2+100y^2-100x+240y-56=0 ?
The solution to 100x^2+100y^2-100x+240y-56=0 is Circle with (a,b)=(1/2 ,-6/5),r= 3/2