What is y^2-x^2-4y+4x-1=0 ?

The solution to y^2-x^2-4y+4x-1=0 is Hyperbola with (h,k)=(2,2),a=1,b=1

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y^2-x^2-4y+4x-1=0

y^{2} - x^{2} - 4 y + 4 x - 1 = 0

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

Solution steps

y^{2} - x^{2} - 4 y + 4 x - 1 = 0

Rewrite

y^{2} - x^{2} - 4 y + 4 x - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

16 y^{2} - 9 x^{2} = 144

4 y^{2} - 4 x^{2} - 24 x + 32 y = - 24

9 x^{2} - 16 y^{2} + 576 = 0

5 x^{2} - 5 y^{2} - 9 x - 14 y + 26 = 0

What is y^2-x^2-4y+4x-1=0 ?
The solution to y^2-x^2-4y+4x-1=0 is Hyperbola with (h,k)=(2,2),a=1,b=1