smismSitlougsyy

2021-11-26

Explain how the rectangular equation $y=5x$ can have infinitely many sets of parametric equations.

Harr1957

Beginner2021-11-27Added 18 answers

Step 1

Given rectangular equation is,

$y=5x$

It represents a line passing through the origin.

Step 2

We find the set of parametric equations by choosing arbitrary parametric equation for x and then substituting it in the given equation.

For example,

Let$x=t$ , then

$y=5t$

Therefore set of parametric equations are$x=t$ and $y=5t$

Now let$x=t+1$ , then

$y=5(t+1)$

$=5t+5$

Therefore set of parametric equations are$x=t+1$ and $y=5t+5$

Similarly by choosing different parametric equation for x, we will get different set of parametric equations.

Hence the rectangular equation$y=5x$ can have infinitely many sets of parametric equations.

Given rectangular equation is,

It represents a line passing through the origin.

Step 2

We find the set of parametric equations by choosing arbitrary parametric equation for x and then substituting it in the given equation.

For example,

Let

Therefore set of parametric equations are

Now let

Therefore set of parametric equations are

Similarly by choosing different parametric equation for x, we will get different set of parametric equations.

Hence the rectangular equation

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