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

The solution to x^2-2y^2-x=1 is Hyperbola with (h,k)=(1/2 ,0),a=(sqrt(5))/2 ,b=(sqrt(5))/(2sqrt(2))

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x^2-2y^2-x=1

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

(h, k) = (\frac{1}{2}, 0), a = \frac{5}{2}, b = \frac{5}{2 2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{5}{2 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{5}{2}, b = \frac{5}{2 2}

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 3 ) ^{2}}{4} = 1

x^{2} - 2 x - 4 y^{2} - 40 y = 103

16 X^{2} - 25 Y^{2} + 96 X + 544 = 0

7 x^{2} - 12 y^{2} - 14 x + 24 y - 28 = 0

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

What is x^2-2y^2-x=1 ?
The solution to x^2-2y^2-x=1 is Hyperbola with (h,k)=(1/2 ,0),a=(sqrt(5))/2 ,b=(sqrt(5))/(2sqrt(2))