What is the center 4x^2-y^2=16 ?

The center 4x^2-y^2=16 is (0,0)

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center 4x^2-y^2=16

center

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

(0, 0)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2, b = 4

And the center is:

(0, 0)

x^{2} - \frac{y ^{2}}{9} = 1

9 x^{2} - 4 y^{2} + 54 x + 8 y + 78 = 0

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

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

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