A curve is defined by the parametric equations x = tē and y = 2t + 1

Find the equation of the tangent at the point where t = 2.

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- Apr 9th 2006, 08:23 PMKiwigirlHelp!
A curve is defined by the parametric equations x = tē and y = 2t + 1

Find the equation of the tangent at the point where t = 2. - Apr 9th 2006, 09:13 PMCaptainBlackQuote:

Originally Posted by**Kiwigirl**

.

We need to find the slope of the tangent, which is , and

to find this we need to use the result that:

So at the slope of the tangent is .

So now we know that the equation of the tangent is of the form:

,

and that at , and , so the tangent passes through the point

, .

Hence:

,

so:

,

and the equation of the tangent is:

.

RonL - Apr 9th 2006, 09:23 PMearbothQuote:

Originally Posted by**Kiwigirl**

as you may know the derivation of parametric(?) functions is done with

So you need the coordinates of the tangent point, which is (4, 5) and the slope, which you calculate with the formula given above:

. With t = 2 you get a slope of 1/2.

Now use the point slope formula of a line:

Greetings

EB - Apr 12th 2006, 01:29 PMKiwigirl
Wow, thank you both for your incredible help, especially for the graph CaptainBlack. I am very impressed :)