What is the center 4x^2-6x+2=y^2-10y ?

The center 4x^2-6x+2=y^2-10y is (3/4 ,5)

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center 4x^2-6x+2=y^2-10y

center

4 x^{2} - 6 x + 2 = y^{2} - 10 y

(\frac{3}{4}, 5)

Solution steps

4 x^{2} - 6 x + 2 = y^{2} - 10 y

Rewrite

4 x^{2} - 6 x + 2 = y^{2} - 10 y

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{( \frac{3 11}{2} ) ^{2}} - \frac{( x - \frac{3}{4} ) ^{2}}{( \frac{3 11}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{4}, 5), a = \frac{3 11}{2}, b = \frac{3 11}{4}

And the center is:

(\frac{3}{4}, 5)

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

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

x^{2} - 16 y^{2} = 144

\frac{( y - \frac{1}{2} ) ^{2}}{2} - \frac{( x + 2 ) ^{2}}{4} = 1

- 9 x^{2} + y^{2} - 72 x - 153 = 0