What is the center x^2+y^2-2x+3y-1=0 ?

The center x^2+y^2-2x+3y-1=0 is (1,-3/2)

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center x^2+y^2-2x+3y-1=0

center

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

Solution steps

x^{2} + y^{2} - 2 x + 3 y - 1 = 0

Rewrite

x^{2} + y^{2} - 2 x + 3 y - 1 = 0

in the form of the standard circle equation

(x - 1)^{2} + (y - (- \frac{3}{2}))^{2} = (\frac{17}{2})^{2}

Therefore the circle properties are:

(a, b) = (1, - \frac{3}{2}), r = \frac{17}{2}

And the center is:

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