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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{5} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

\frac{( x - 8 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{9 + y ^{2}} = 1

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

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