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Exercises Trigonometry

Example 6 from Algebra and Trigonometry, 10.6 Parametric Equations

Eliminating the Parameter in Logarithmic Equations

Eliminate the parameter and write as a Cartesian equation: $x (t) = \sqrt{t} + 2$ and $y (t) = \log (t) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Solve the first equation for $t .$

$\begin{array}{l} x = \sqrt{t} + 2 \\ x - 2 = \sqrt{t} \\ {(x - 2)}^{2} = t & Square both sides . \end{array}$
Then, substitute the expression for $t$ into the $y$ equation.
$\begin{array}{l} y = \log (t) \\ y = \log {(x - 2)}^{2} \end{array}$

The Cartesian form is $y = \log {(x - 2)}^{2} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Eliminate the parameter and write as a rectangular equation.

\begin{array}{l} x (t) = t^{2} \\ y (t) = \ln t t > 0 \end{array}

How did it go?

PreviousEliminating the Parameter in Exponential Equations Next Eliminating the Parameter from a Pair of Trigonometric Parametric Equations

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.6, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.