1. ## Hyperbolas

I need help graphing a hyperbola not in standard form. I don't understand how to use the squaring method (I'm pretty sure we haven't learned that yet). The equation is 4y^2 - 9x^2 = 1.

2. Originally Posted by bandgeek
I need help graphing a hyperbola not in standard form. I don't understand how to use the squaring method (I'm pretty sure we haven't learned that yet). The equation is 4y^2 - 9x^2 = 1.

The standard form of a hyperbola is

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

so we are really close to what we need
we need to get the four into the denominator some how? hmmm..

lets try an experiment....

$\displaystyle 4=\frac{4}{1}=\frac{\frac{1}{4}\cdot 4}{\frac{1}{4}}=\frac{1}{\frac{1}{4}}$

using this one the above we get

$\displaystyle \frac{y^2}{\frac{1}{4}}-\frac{x^2}{\frac{1}{9}}=1$

Now we just need to write them as squares so we get

$\displaystyle \frac{y^2}{\left(\frac{1}{2}\right)^2}-\frac{x^2}{\left(\frac{1}{3}\right)^2}=1$

I hope this helps.