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

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

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2y^2-4x^2=1

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{4} - \frac{( y - 6 ) ^{2}}{140} = 1

\frac{y ^{2}}{49} - \frac{x ^{2}}{36} = 1

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

4 x^{2} - y^{2} - 36 = 0

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

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