1. Parametric Equations

Hi all, first time poster but if this goes well will probably be seeking out more help.

So we are doing parametric equations and I understand how to find the slope, however from their I'm totally lost. >.<

Please don't just answer, I have an exam soon and if you could explain why, it would be wonderful.

The original question is:
Find an equation of the tangent line to this curve

x=(t^2)-8t
y=(t^2)+7t

So I know you take the derivative of both sides to find dx/dt and dy/dt

dx/dt=2t-8
dy/dt=2t+7

So the slope is equal to...

(2t+7)/(2t-8)

The T value they give is 8/2 (4?)

So..

2(4)+7/2(4)-8
15/0

Slope is undefined....

From there I have no idea

_______________________

However if the slope were to work, such as with this equation...

x=(t^3)-3t
y=t^2
@ t= 3

I get the slope 1/4

so
y=(x/4)+b

However, I don't know what values to put for x and y!!

Anyway. Thank you for any help.

2. Originally Posted by Khart
However if the slope were to work, such as with this equation...

x=(t^3)-3t
y=t^2
@ t= 3

I get the slope 1/4

so
y=(x/4)+b

However, I don't know what values to put for x and y!!

Anyway. Thank you for any help.
Put t = 3 in the parametric equation to get the value(s) of x and y.

x=(3^3)-3(3)
y=(3)^2

3. You need to post the whole problem using the exact wording.

4. That is the whole problem =o

Its an online assignment so the descriptions are a bit low.

5. Well, the value of T they gave is strange... how did they gave the problem question?

6. If you mean that there is a text box with "8/2" for t then I would be inclined to guess that they are giving you two problems and asking for the tangent line at both t= 8 and t= 2.

7. I know its strange! Its Wiley Plus which is honestly the worst online homework in the world.

I wrote it down word for word.

8. Originally Posted by Khart
Hi all, ...
...
The original question is:
Find an equation of the tangent line to this curve

x=(t^2)-8t
y=(t^2)+7t

So I know you take the derivative of both sides to find dx/dt and dy/dt

dx/dt=2t-8
dy/dt=2t+7

So the slope is equal to...

(2t+7)/(2t-8)

The T value they give is 8/2 (4?)

So..

2(4)+7/2(4)-8
15/0

Slope is undefined....

From there I have no idea

...
All your calculations and considerations are OK!

1. Calculate the coordinates of the tangent point $T(x_T, y_T)$.

2. If the slope is undefined then the equation of the tangent is $x = x_T$