What is the center x^2-y^2-4x+8y-21=0 ?

The center x^2-y^2-4x+8y-21=0 is (2,4)

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center x^2-y^2-4x+8y-21=0

center

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

(2, 4)

Solution steps

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

Rewrite

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 4), a = 3, b = 3

And the center is:

(2, 4)

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

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