What is the center 4x^2-y^2+8x-2y+7=0 ?

The center 4x^2-y^2+8x-2y+7=0 is (-1,-1)

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center 4x^2-y^2+8x-2y+7=0

center

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

(- 1, - 1)

Solution steps

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

Rewrite

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(- 1, - 1)

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

x^{2} - 16 y^{2} = 144

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

- 9 x^{2} + y^{2} - 72 x - 153 = 0

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{8 ^{2}} = 1

What is the center 4x^2-y^2+8x-2y+7=0 ?
The center 4x^2-y^2+8x-2y+7=0 is (-1,-1)