What is the center 3x^2-15x=-3y^2 ?

The center 3x^2-15x=-3y^2 is (5/2 ,0)

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center 3x^2-15x=-3y^2

center

3 x^{2} - 15 x = - 3 y^{2}

(\frac{5}{2}, 0)

Solution steps

3 x^{2} - 15 x = - 3 y^{2}

Rewrite

3 x^{2} - 15 x = - 3 y^{2}

in the form of the standard circle equation

(x - \frac{5}{2})^{2} + (y - 0)^{2} = (\frac{5}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{5}{2}, 0), r = \frac{5}{2}

And the center is:

(\frac{5}{2}, 0)

(x - 3)^{2} + y^{2} = 16

x^{2} - 4 x + y^{2} = 21

4 x^{2} + 4 y^{2} + 6 x + 8 y - 5 = 0

x^{2} + y^{2} + 14 x + 16 y + 14 = 0

5 x^{2} + 5 y^{2} + 10 x - 5 y + 3 = 0