# Parametric Quadratic Curve and Geometric Slope

• Oct 10th 2009, 03:39 PM
jpezze
Parametric Quadratic Curve and Geometric Slope
If any information on this problem, would be greatly appreciated.

A parametric Quadratic curve passes through the points (0,0) (4,3) (4,-3) which are parameterized at u=0, 0.5, 1 respectively. Determine the geometric slope dy/dx at each end.

Thanks
• Oct 11th 2009, 05:40 AM
Coomast
Quote:

Originally Posted by jpezze
If any information on this problem, would be greatly appreciated.

A parametric Quadratic curve passes through the points (0,0) (4,3) (4,-3) which are parameterized at u=0, 0.5, 1 respectively. Determine the geometric slope dy/dx at each end.

Thanks

Hello jpezze,

The solution is not that difficult. Consider the general quadratic parameteric equation, it is:

$x=a \cdot u^2+b \cdot u+c$
$y=d \cdot u^2+e \cdot u+f$

Putting the origin into this system you need to have c=0 and f=0, making things a bit easier. Now putting the other two points in this system gives you a system of four equations with four unknowns (a,b,d,e). Solving this system gives you the equation of the curve, I got:

$x=-8 \cdot u^2+12 \cdot u$
$y=-18 \cdot u^2+15 \cdot u$

Do this calculation yourself and make sure I did not make a mistake. Now the derivative can be found using the chain rule like:

$\frac{dy}{dx}=\frac{dy}{du} \cdot \frac{du}{dx}$

Using now the equation of the curve and putting everything in there you have for the slope:

$\frac{dy}{dx}=\frac{-36 \cdot u+15}{-16\cdot u+12}$

Putting the values of 0, 1/2 and 1 in there you have your solution. I added a small picture to make things more clear but make sure you do this calculation and come back if you have any questions.

best regards,

coomast
• Oct 11th 2009, 11:01 AM
jpezze
Thank You very much, that really helped out. I also have similar questions dealing with parametric curves in other advance topics and advance applied math. If you have a suggestion of where I should post these instead of the Differential Equations subforum that would be great thanks, because i really do need help on this matter of subect, but thank you again.
• Oct 12th 2009, 10:24 AM
Coomast
Quote:

Originally Posted by jpezze
Thank You very much, that really helped out. I also have similar questions dealing with parametric curves in other advance topics and advance applied math. If you have a suggestion of where I should post these instead of the Differential Equations subforum that would be great thanks, because i really do need help on this matter of subect, but thank you again.

You're welcome....
I would put it in the calculus section.

best regards,

coomast