1. ## 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

2. 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:

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

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:

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

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

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

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

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

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

3. 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.

4. 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