 # Explain and solve how the rectangular equation y = 5x can have infinitely many sets of parametric equations. waigaK 2020-10-20 Answered
Explain and solve how the rectangular equation $y=5x$ can have infinitely many sets of parametric equations.
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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 . Now let , then
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 $y=5x$ can have infinitely many sets of parametric equations.