What is the center y^2-4x^2-16x-2y-19=0 ?

The center y^2-4x^2-16x-2y-19=0 is (-2,1)

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center y^2-4x^2-16x-2y-19=0

center

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

(- 2, 1)

Solution steps

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

Rewrite

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 1), a = 2, b = 1

And the center is:

(- 2, 1)

5 x^{2} - 4 y^{2} - 20 x - 8 y - 4 = 0

0 = 9 y^{2} - x^{2} + 2 x + 72 y + 125

9 x^{2} - 9 y^{2} - 18 x + 54 = 0

\frac{( x - 3 ) ^{2}}{49} - \frac{( y - 5 ) ^{2}}{25} = 1

(\frac{y - 1}{9})^{2} - (\frac{x - ( - 2 )}{4})^{2} = 1

What is the center y^2-4x^2-16x-2y-19=0 ?
The center y^2-4x^2-16x-2y-19=0 is (-2,1)