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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x - y - 3) \cdot (x + y + 3) = 16

y^{2} - 3 y - 2 = x^{2}

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

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

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