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

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

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

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

(h, k) = (1, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

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

4 x^{2} - 25 (y - 1)^{2} = 100

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

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

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