Hyperbola and Elipse Equations

Nov 2009
7
0
Need help with these...or more like I forget algebra.

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

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

Thanks.
 
Nov 2009
717
133
Wahiawa, Hawaii
\(\displaystyle 4y^2 - x^2 = 1\)
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 \(\displaystyle b^2 = a^2 - c^2\)
\(\displaystyle a > b, a > c\)
 
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Nov 2009
7
0
Yeah, so I have to eliminate the coefficient. Thats' what I can't remember how to do.
 
Nov 2009
717
133
Wahiawa, Hawaii
basically
complete the square
 
Nov 2009
7
0
basically
complete the square
Actually I remembered, as obvious as it seems...

\(\displaystyle 4y^2\) = \(\displaystyle \frac{y^2}{\frac{1}{4}}\) = \(\displaystyle \frac{y^2}{\frac{1}{2}^2}\)