Precalculus Examples

x = t^{2}

$x = t^{2}$ ,

y = t^{4} + 1

$y = t^{4} + 1$

Step 1

Set up the parametric equation for

x (t)

$x (t)$ to solve the equation for

t

$t$ .

x = t^{2}

$x = t^{2}$

Step 2

Rewrite the equation as

t^{2} = x

$t^{2} = x$ .

t^{2} = x

$t^{2} = x$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

t = \pm \sqrt{x}

$t = \pm \sqrt{x}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

t = \sqrt{x}

$t = \sqrt{x}$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

t = - \sqrt{x}

$t = - \sqrt{x}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

t = \sqrt{x}

$t = \sqrt{x}$

t = - \sqrt{x}

$t = - \sqrt{x}$

t = \sqrt{x}

$t = \sqrt{x}$

t = - \sqrt{x}

$t = - \sqrt{x}$

Step 5

Replace

t

$t$ in the equation for

y

$y$ to get the equation in terms of

x

$x$ .

y = {(\sqrt{x}, - \sqrt{x})}^{4} + 1

$y = {(\sqrt{x}, - \sqrt{x})}^{4} + 1$

x = t^{2}, y = t^{4} + 1

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

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