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 $1$ .

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

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 $2$ .

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