# Math Help - Math function for parabola

1. ## Math function for parabola

Hello. I need to find an implicit function that plots a parabolic tube with a circular cross-section of radius 3. Even if you know only the function of the parabola, it would be a great hint.

Thank you in advance.

EDIT: well, first post, first wrong forum. I think this should go in the trigonometry forum.

2. ## Re: Math function for parabola

Originally Posted by TyTiKi
Hello. I need to find an implicit function that plots a parabolic tube with a circular cross-section of radius 3. Even if you know only the function of the parabola, it would be a great hint.

Thank you in advance.

EDIT: well, first post, first wrong forum. I think this should go in the trigonometry forum.
Let x = t. Then the orange line consists of all points (t, t, 0)

The length of the orange line segment from (0, 0, 0) to (85, 85, 0) is $85 \cdot \sqrt{2}$

The equation of a parabola with it's vertex at (0, 0, 30) is

$p=a \cdot s^2 + 30$

where s is the unit on the orange line when x and y increases by 1. So $s = t \cdot \sqrt{2}$

Determine the value of a if p = 0 at (85, 85, 0).

I've got $a = -\frac3{1445}$

So the equation of the parabola is $p:\left\lbrace\begin{array}{l}x = t \\ y = t \\ z = -\frac6{1445}(t )^2+30 \end{array}\right.$

3. ## Re: Math function for parabola

Thank you very much for your help earboth. However I need an implicit function that I could write in Imp View 3D.

It would be fantastic if you could help me.

4. ## Re: Math function for parabola

I found a way.

(0.75-sqrt(y^2+z^2/3))^2+x^2<0.030

gives me a parabolic tube. Now I need something that rotates it by 45 degrees. Any hint?