What is the center 16y^2-25x^2=400 ?

The center 16y^2-25x^2=400 is (0,0)

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center 16y^2-25x^2=400

center

16 y^{2} - 25 x^{2} = 400

(0, 0)

Solution steps

16 y^{2} - 25 x^{2} = 400

Rewrite

16 y^{2} - 25 x^{2} = 400

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{5 ^{2}} - \frac{( x - 0 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 5, b = 4

And the center is:

(0, 0)

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

9 x^{2} - y^{2} - 72 x + 8 y + 119 = 0

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

x^{2} - y^{2} - 6 x = 16

\frac{( y - 4 ) ^{2}}{81} - \frac{( x + 5 ) ^{2}}{36} = 1