# HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal vect

1. Jul 12, 2011

### soccer*star

Consider the hyperbola y^2-x^2=1 (y>0)
a.) Find a parameterization for the curve and write it in vector form, R(t)
(b) Calculate the unit tangent vector as a function of the parameter.
(c) Calculate the unit normal vector and the curvature vector as a function of the parameter.

2. Jul 12, 2011

### micromass

Staff Emeritus
Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

You must find function f and g such that

$$f(t)^2-g(t)^2=1$$

3. Jul 12, 2011

### soccer*star

Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

I tried to set x=t and y= sqrrt(1+t^2) ...it comes out nasty and ugly, so ugly that i didn't even finish it..i'm not sure if there's a better way to do it.

4. Jul 12, 2011

### ilsdcls

Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

soccer*star, is this problem due tomorrow by any chance?

5. Jul 13, 2011

### micromass

Staff Emeritus
Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

If you would have $x^2+y^2=1$, then there's an easy choice:

$$\sin^2(t)+\cos^2(t)=1$$

But now you have $x^2-y^2=1$. Can you do something similar?