# Hyperbola and Elipse Equations

• Nov 12th 2009, 07:38 AM
Mr.Berlin
Hyperbola and Elipse Equations
Need help with these...or more like I forget algebra.

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

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

Thanks.
• Nov 12th 2009, 08:48 AM
bigwave
$\displaystyle 4y^2 - x^2 = 1$
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 $\displaystyle b^2 = a^2 - c^2$
$\displaystyle a > b, a > c$
• Nov 12th 2009, 12:40 PM
Mr.Berlin
Yeah, so I have to eliminate the coefficient. Thats' what I can't remember how to do.
• Nov 12th 2009, 12:51 PM
bigwave
basically
complete the square
• Nov 12th 2009, 01:23 PM
Mr.Berlin
Quote:

Originally Posted by bigwave
basically
complete the square

Actually I remembered, as obvious as it seems...

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