# Hyperbola and Elipse Equations

#### Mr.Berlin

Need help with these...or more like I forget algebra.

$$\displaystyle 4y^2 - x^2 = 1$$

$$\displaystyle 4y^2 + x^2 = 1$$

Thanks.

#### bigwave

$$\displaystyle 4y^2 - x^2 = 1$$
this is a hyperbola with the foci on the y axis
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 $$\displaystyle b^2 = a^2 - c^2$$
$$\displaystyle a > b, a > c$$

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• Mr.Berlin

#### Mr.Berlin

Yeah, so I have to eliminate the coefficient. Thats' what I can't remember how to do.

#### bigwave

basically
complete the square

#### Mr.Berlin

basically
complete the square
Actually I remembered, as obvious as it seems...

$$\displaystyle 4y^2$$ = $$\displaystyle \frac{y^2}{\frac{1}{4}}$$ = $$\displaystyle \frac{y^2}{\frac{1}{2}^2}$$