What is the center x^2+y^2=-4x+3y ?

The center x^2+y^2=-4x+3y is (-2, 3/2)

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center x^2+y^2=-4x+3y

center

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

(- 2, \frac{3}{2})

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

And the center is:

(- 2, \frac{3}{2})

(x + 4)^{2} + (y - 10)^{2} = 274

x^{2} + y^{2} - 10 x + 12 y + 25 = 0

y^{2} + x^{2} - 12 x + 18 y + 116 = 0

16 x^{2} + 16 y^{2} + 8 x - 3 y = - 1

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