Explain how the rectangular equation y=5x can have infinitely many

smismSitlougsyy

smismSitlougsyy

Answered question

2021-11-26

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

Answer & Explanation

Harr1957

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.

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