What is the center 25x^2-4y^2-100x-16y-16=0 ?

The center 25x^2-4y^2-100x-16y-16=0 is (2,-2)

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center 25x^2-4y^2-100x-16y-16=0

center

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

(2, - 2)

Solution steps

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

Rewrite

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 2), a = 2, b = 5

And the center is:

(2, - 2)

9 x^{2} - 16 y^{2} - 36 x + 96 y + 252 = 0

5 y^{2} - 16 x^{2} + 400 = 0

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

x^{2} - y^{2} + 6 x + 10 y = 2

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{16} = 1

What is the center 25x^2-4y^2-100x-16y-16=0 ?
The center 25x^2-4y^2-100x-16y-16=0 is (2,-2)