What is the center 5x^2-4y^2-20x-8y-4=0 ?

The center 5x^2-4y^2-20x-8y-4=0 is (2,-1)

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center 5x^2-4y^2-20x-8y-4=0

center

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

(2, - 1)

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 1), a = 2, b = 5

And the center is:

(2, - 1)

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

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

What is the center 5x^2-4y^2-20x-8y-4=0 ?
The center 5x^2-4y^2-20x-8y-4=0 is (2,-1)