y^2=2x^2-1

Solution

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

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

Solution steps

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

Rewrite

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

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

3 y^{2} - 6 x^{2} - 12 = 0

9 x^{2} - 16 y^{2} - 144 = 0

(x + 2)^{2} - y^{2} = 8

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

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

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