What is the center x^2-y^2=10(x-y)+1 ?

The center x^2-y^2=10(x-y)+1 is (5,5)

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center x^2-y^2=10(x-y)+1

center

x^{2} - y^{2} = 10 (x - y) + 1

(5, 5)

Solution steps

x^{2} - y^{2} = 10 (x - y) + 1

Rewrite

x^{2} - y^{2} - 10 (x - y) - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, 5), a = 1, b = 1

And the center is:

(5, 5)

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

9 x^{2} - 16 y^{2} - 144 = 0

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

9 x^{2} - 16 y^{2} - 126 x + 160 y - 103 = 0

\frac{( x - h ) ^{2}}{64} - \frac{( y - k ) ^{2}}{9} = 1