Precalculus Examples

$x = 3 t$ ,

$y = t^{2}$

Step 1

Set up the parametric equation for

$x (t)$ to solve the equation for

$t$ .

$x = 3 t$

Step 2

Rewrite the equation as

$3 t = x$ .

$3 t = x$

Step 3

Divide each term in

$3 t = x$ by

$3$ and simplify.

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Step 3.1

Divide each term in

$3 t = x$ by

$3$ .

$\frac{3 t}{3} = \frac{x}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 t}{3} = \frac{x}{3}$

Step 3.2.1.2

Divide

$t$ by

$1$ .

$t = \frac{x}{3}$

$t = \frac{x}{3}$

$t = \frac{x}{3}$

$t = \frac{x}{3}$

Step 4

Replace

$t$ in the equation for

$y$ to get the equation in terms of

$x$ .

$y = {(\frac{x}{3})}^{2}$

Step 5

Simplify

${(\frac{x}{3})}^{2}$ .

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Step 5.1

Apply the product rule to

$\frac{x}{3}$ .

$y = \frac{x^{2}}{3^{2}}$

Step 5.2

Raise

$3$ to the power of

$2$ .

$y = \frac{x^{2}}{9}$

$y = \frac{x^{2}}{9}$

$x = 3 t, y = t^{2}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$