\(\displaystyle 4y^2 - x^2 = 1\)

this is a hyperbola with the foci on the y axis

you can ussually tell by the - sign in between

the general equation is:

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

where \(\displaystyle b^2 = c^2 - a^2\)

\(\displaystyle c > a, c > b\)

\(\displaystyle 4y^2+ x^2 = 1\)

this is an ellipse

the general equation is:

\(\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

where \(\displaystyle b^2 = a^2 - c^2\)

\(\displaystyle a > b, a > c\)