Working with parametric equations Consider

Chapter 8, Problem 14E

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QUESTION:

Consider the following parametric equations.

a. Eliminate the parameter to obtain an equation in x and y.

b. Describe the curve and indicate the positive orientation.

\(x=e^{2t},\ y=e^t+1;\ 0\ \leq\ t\ \leq\ 25\)

Questions & Answers

QUESTION:

Consider the following parametric equations.

a. Eliminate the parameter to obtain an equation in x and y.

b. Describe the curve and indicate the positive orientation.

\(x=e^{2t},\ y=e^t+1;\ 0\ \leq\ t\ \leq\ 25\)

ANSWER:

Solution 14EStep 1:a. Eliminate the parameter to obtain an equation in x and y.Given x = e2t, y = et + 1Take natural logarithm on both sides we get,Put in y = et + 1By using we get

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