
Hyperbolas.
I know how to write the equation of a hyperbola with its two branches (i.e. x^2/a^2y^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?

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

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

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

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