What is X^2+Y^2+2X-3Y=0 ?

The solution to X^2+Y^2+2X-3Y=0 is Circle with (a,b)=(-1, 3/2),r=(sqrt(13))/2

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X^2+Y^2+2X-3Y=0

X^{2} + Y^{2} + 2 X - 3 Y = 0

(a, b) = (- 1, \frac{3}{2}), r = \frac{13}{2}

Solution steps

X^{2} + Y^{2} + 2 X - 3 Y = 0

Rewrite

X^{2} + Y^{2} + 2 X - 3 Y = 0

in the form of the standard circle equation

(X - (- 1))^{2} + (Y - \frac{3}{2})^{2} = (\frac{13}{2})^{2}

Therefore the circle properties are:

(a, b) = (- 1, \frac{3}{2}), r = \frac{13}{2}

x^{2} + (y - \frac{7}{2})^{2} = 81

(x + 4)^{2} + (y + 3)^{2} = 36

x^{2} + y^{2} - 14 x - 8 y = 0

x^{2} + y^{2} = 4 y + 3

2 x^{2} + 2 y^{2} = 12 y - 10

What is X^2+Y^2+2X-3Y=0 ?
The solution to X^2+Y^2+2X-3Y=0 is Circle with (a,b)=(-1, 3/2),r=(sqrt(13))/2