waigaK

2020-10-20

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

Asma Vang

Skilled2020-10-21Added 93 answers

Step 1
$y=5x$
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 $x=t\text{}and\text{}y=5t$ .
Now let $x=t\text{}+\text{}1$ , then
$y=5(t\text{}+\text{}1)$

$=5t\text{}+\text{}5$
Therefore set of parametric equations are $x=t\text{}+\text{}1\text{}and\text{}y=5t\text{}+\text{}5$ .
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.

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