# Math Help - Hyperbolas.

1. ## Hyperbolas.

I know how to write the equation of a hyperbola with its two branches (i.e. x^2/a^2-y^2/b^2=1 or vice versa), but can you write the equation of just one branch of the hyperbola? Would it just be the equation of a parabola?

I know you could restrict the domain for those with horizontal transverse axes, but what about for vertical or in general?

2. ## Re: Hyperbolas.

Your hyperbola equation is centred at (0,0) so you can restrict the domain as x>0 or x<0.

3. ## Re: Hyperbolas.

Thanks, I understand that, but what if the transverse axis is vertical and I only want the top branch?

4. ## Re: Hyperbolas.

O.k, you require a hyperbola that opens up top and bottom, which is $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ which is also centred at the origin, you can restrict $y>0$

5. ## Re: Hyperbolas.

And, in fact, for y> 0, you can solve for y: $y= a\sqrt{1- \frac{x^2}{b^2}}$.