Calculus Examples

$x = \frac{1}{4} t$ , $y = t^{2}$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = \frac{1}{4} t$

Step 2

Rewrite the equation as $\frac{1}{4} t = x$ .

$\frac{1}{4} t = x$

Step 3

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} t) = 4 x$

Step 4

Simplify the left side.

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Step 4.1

Simplify $4 (\frac{1}{4} t)$ .

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Step 4.1.1

Combine $\frac{1}{4}$ and $t$ .

$4 \frac{t}{4} = 4 x$

Step 4.1.2

Cancel the common factor of $4$ .

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Step 4.1.2.1

Cancel the common factor.

$4 \frac{t}{4} = 4 x$

Step 4.1.2.2

Rewrite the expression.

$t = 4 x$

Step 5

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

$y = {(4 x)}^{2}$

Step 6

Simplify ${(4 x)}^{2}$ .

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Step 6.1

Apply the product rule to $4 x$ .

$y = 4^{2} x^{2}$

Step 6.2

Raise $4$ to the power of $2$ .

$y = 16 x^{2}$