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

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

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

center

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

(- 3, 5)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{( 14 ) ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{( 14 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 5), a = 14, b = 14

And the center is:

(- 3, 5)

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{16} = 1

y^{2} - x^{2} = \frac{1}{25}

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

\frac{( x + 1 ) ^{2}}{36} - \frac{( y - 3 ) ^{2}}{25} = 1